28. [Area / Volume] cm 2. in = =

Size: px
Start display at page:

Download "28. [Area / Volume] cm 2. in = ="

Transcription

1 8. [ / Volume] Skill 8. Calculating the area of polygons by counting squares and triangles on a square grid (). Count the number of fully shaded squares on the grid. If necessary add on the number of half shaded squares (or triangles). Look for short cuts in your counting. Hint: To calculate the area of a rectangular shape it is possible to count the number of squares in a row and then multiply by the number of squares in a column. Q. Find the area of the rectangle. A. 6 There are 6 squares in a row cm and squares in a column. cm continues on page 66 MMBlue MMGreen cm a) Find the area of the triangle. b) Find the area of the rectangle. cm cm cm cm c) Find the area of the rectangle. d) Find the area of the rectangle. cm 0.5 in. cm in. page 65 Math s Mate Blue/Green Skill Builder 8

2 Skill 8. Calculating the area of polygons by counting squares and triangles on a square grid (). e) Find the area of the rectangle. f) Find the area of the polygon. continued from page 65 MMBlue MMGreen in. cm cm in. g) Find the area of the trapezoid. h) Find the area of the triangle. cm 0.5 in. cm in. i) Find the area of the parallelogram. j) Find the area of the trapezoid. cm cm cm cm page 66 Math s Mate Blue/Green Skill Builder 8

3 Skill 8. Comparing the area of polygons on a square grid (). Break the shape up into rectangles and triangles if necessary. Calculate the area of any rectangle by: Counting the squares OR Multiplying the number of squares in a row by the number of squares in a column. Calculate the area of any triangle by halving the area of the rectangle that would enclose it. Compare your results. Q. Do the rectangle and the triangle have the same area? A. A B No A 6 sq. units continues on page 68 MMBlue MMGreen A enclosing rectangle 3 B sq. units 3 B a) Do these rectangles have the same area? b) Do these rectangles have the same area? 4 A B A B yes 5 A... B... c) Do these polygons have the same area? d) Do these triangles have the same area? A... B... A... B... page 67 Math s Mate Blue/Green Skill Builder 8

4 Skill 8. Comparing the area of polygons on a square grid (). continued from page 67 MMBlue MMGreen e) Do these triangles have the same area? f) Do these triangles have the same area? A... B... A... B... g) Do these triangles have the same area? h) Do these triangles have the same area? i) Do these polygons have the same area? j) Do these polygons have the same area? k) Do the square and the parallelogram have the same area?... l) Do the parallelogram and the kite have the same area? page 68 Math s Mate Blue/Green Skill Builder 8

5 Skill 8.3 Estimating the area of irregular shapes on a square grid. MMBlue MMGreen Break the shape up into workable parts (rectangles/triangles/curved shapes). Calculate the area of any rectangle by: Counting the squares OR Multiplying the number of squares in a row by the number of squares in a column. Calculate the area of any triangle by halving the area of the rectangle that would enclose it. Estimate the area of any partly curved shape by making up whole squares from the shaded region. Add the results. Q. Find the area of the shaded shape. [Round to the nearest whole number.] A. A + B sq. units A 4 whole units A B 9 units (made up from part units) B a) Find the area of the shaded shape. [Round to the nearest whole number.] b) Find the area of the shaded shape. [Round to the nearest whole number.] A B A 7 and B... A + B sq. units A and B... A + B... sq. units c) Find the area of the shaded shape. [Round to the nearest whole number.] d) Find the area of the shaded shape. [Round to the nearest whole number.] sq. units sq. units page 69 Math s Mate Blue/Green Skill Builder 8

6 Skill 8.4 Calculating the area of squares, rectangles and parallelograms (). Use the appropriate formula. square A l l l Q. Using A lw find the area of the rectangle. 6 cm l length rectangle A l w lw. l length w width parallelogram A b h bh A. A lw where l 6 and w cm b base continues on page 7 MMBlue MMGreen h height a) Using length width find the area of this rectangle. b) Using length width find the area of this rectangle. cm cm 6 cm 7 cm A 7 cm A cm c) Using base height find the area of this parallelogram. d) Using base height find the area of this parallelogram. cm A cm A cm e) Using length width find the area of this rectangle. 0.5 in. f) Using A lw find the area of the rectangle. mm in. 50 mm A in. A mm page 70 Math s Mate Blue/Green Skill Builder 8

7 Skill 8.4 Calculating the area of squares, rectangles and parallelograms (). g) Using length length find the area of the square. continued from page 70 MMBlue MMGreen h) Using l find the area of this square..5 in. cm A A in. i) Find the area of the square. j) Using base height find the area of the parallelogram. 0 mm 3.. mm A A cm k) Using base height find the area of the parallelogram. l) Using A lw find the area of the rectangle. 0 mm 6 mm 40 mm b 60 mm mm A A mm m) Using A bh find the area of the parallelogram. 55 mm 0 mm n) Find the area of this parallelogram. 0 mm 36 mm mm A A mm page 7 Math s Mate Blue/Green Skill Builder 8

8 Skill 8.5 Calculating the area of triangles (). Use the formula. Q. Using base height find the area of the triangle. cm triangle b base h height A b h bh A. A bh where b 6 and h 6 6 cm continues on page 73 MMBlue MMGreen cm a) Using base height find the area of the triangle. in. b) Using base height find the area of the triangle. in. 7 cm A... 4 in. c) Using base height find the area of the triangle. A... cm d) Using A bh find the area of the right triangle. 50 mm 5 mm A... A... cm mm page 7 Math s Mate Blue/Green Skill Builder 8

9 Skill 8.5 Calculating the area of triangles (). e) Using base height find the area of the triangle. continued from page 7 MMBlue MMGreen f) Using bh find the area of the triangle.. 5 mm 0 mm A... A... cm mm g) Using base height find the area of the triangle. h) Using bh find the area of the triangle. cm 7. A... 0 mm 40 mm A... cm mm i) Using bh find the area of the triangle. 0 mm j) Using bh find the area of the triangle. 55 mm 7 mm 30 mm A... A... mm mm page 73 Math s Mate Blue/Green Skill Builder 8

10 Skill 8.6 Calculating the volume of rectangular prisms by counting cubes (). Count the cubes. Hint: Count the cubes in one layer and then multiply the result by the total number of layers. continues on page 75 MMBlue MMGreen Q. Find the volume of the rectangular prism. A. V cubes in top layer 5 layers all together Vol 8 cm cm a) Find the volume of the rectangular prism. b) If 4 boxes can fit inside these shelves, find the total volume of the boxes. Vol box Vol 50 in. 3 6 cm V 4 3 V in. 3 c) Find the volume of the rectangular prism. d) Find the volume of the rectangular prism. Vol cm 0 cm Vol V V e) Find the volume of the rectangular prism. f) Find the volume of the rectangular prism. Vol cm Vol 9 cm V V page 74 Math s Mate Blue/Green Skill Builder 8

11 Skill 8.6 Calculating the volume of rectangular prisms by counting cubes (). continued from page 74 MMBlue MMGreen g) Find the volume of the rectangular prism. h) Find the volume of the rectangular prism. Vol 8 cm Vol 6 cm V V i) Find the volume of the rectangular prism. j) Find the volume of the rectangular prism. Vol 9 cm Vol 0 cm V V k) Find the volume of the rectangular prism. l) Find the volume of the rectangular prism. Vol 9 cm Vol 7 cm V V page 75 Math s Mate Blue/Green Skill Builder 8

12 Skill 8.7 Calculating the volume of square and rectangular prisms (). Use the appropriate formula. cube V l l l l 3 square prism V l l h l h l length h height l length rectangular prism V l w h lwh continues on page 77 MMBlue MMGreen h height w width l length Q. Using V l h find the volume of the square prism.. A. V a) Using V lwh find the volume of the rectangular prism. b) Using V l h find the volume of the square prism. 0 mm 70 mm mm l cm h V ,800 mm 3 V... c) Using V l h find the volume of the square prism. d) Using V l 3 find the volume of the cube. l 0 mm in. V in. V... in. 3 mm 3 page 76 Math s Mate Blue/Green Skill Builder 8

13 Skill 8.7 Calculating the volume of square and rectangular prisms (). e) Using V lwh find the volume of the bank of lockers that is a rectangular prism. 6 ft 0 ft ft V... ft 3 f) Using V lwh find the volume of the rectangular prism. 60 mm V... continued from page 76 MMBlue MMGreen mm 5 mm mm 3 g) Using V l 3 find the volume of the cube. h) Using V lwh find the volume of the rectangular prism. 5 mm V... i) Using V l h find the volume of the square prism. mm 3. V... j) Using V l h find the volume of the square prism. l. h cm l 30 mm V... h 0 mm V... mm 3 page 77 Math s Mate Blue/Green Skill Builder 8

14 Skill 8.8 Calculating the area of composite shapes (). Break the shape up into workable parts (rectangles/triangles). Calculate the area of each part. (see skill 8.4, page 70 and skill 8.6, page 74) Add the results. continues on page 79 MMBlue MMGreen Q. Find the area of the shaded polygon. A. A lw where l 4 and w A bh where b 5 and h A 3 bh where b 3 and h A A + A + A sq. units A A A 3 a) Find the area of the shaded polygon. b) Find the area of the shaded polygon. 3. cm cm 3. cm cm cm A A A A... A cm A A... A sq. units c) Find the area of the shaded polygon. d) Find the area of the shaded polygon. A A... A sq. units A A... A sq. units page 78 Math s Mate Blue/Green Skill Builder 8

15 Skill 8.8 Calculating the area of composite shapes (). continued from page 78 MMBlue MMGreen e) Find the area of the shaded polygon. f) Find the area of the shaded polygon. A A... A A A sq. units... A sq. units g) Find the area of the bowtie. h) Find the area of the polygon. 8 cm 0 cm A A... A... cm cm A A... A... cm i) Find the area of the shaded polygon. j) Find the area of the polygon. 0 mm in. mm 7 mm mm.5 in. in. A A A A A... mm A in.... page 79 Math s Mate Blue/Green Skill Builder 8

16 Skill 8.9 Calculating the area of trapezoids and rhombii. Use the appropriate formula. trapezoid b h a A (base a + base b) height h (a + b)h Q. Using A (a + b)h find the area of the trapezoid. cm 6 cm rhombus A diagonal a diagonal b ab continues on page 8 A. A (a + b)h where a 3, b 6 and h (6 + 3) 9 9 cm a b l MMBlue MMGreen a) Using A ab find the area of the rhombus. A mm c) Using A (a + b)h find the area of the trapezoid. b 6 cm cm 4 mm a 56 mm A... cm b) Using (base a + base b) height find the area of the trapezoid. a 30 mm 0 mm b 45 mm A... mm d) Using diagonal a diagonal b find the area of the rhombus. a 50 mm b 5 mm A... mm page 80 Math s Mate Blue/Green Skill Builder 8

17 Skill 8.0 Calculating the area of circles and composite circular shapes. Use the formula. Hint: If you are given the diameter then halve to find the radius: Q. Using A πr and π 3.4, find the area of the semi-circle. 0 mm circle a) Using A πr and π 3.4, find the area of the shaded shape. 6 cm cm radius A π radius radius where π πr or 7 d r MMBlue MMGreen A. of circle πr where d 0 and r of semi-circle mm d r b) Using A πr and π, find the area of the circle. 7 6 cm A cm mm A If d 6 then r 3 A A 6 6 and using A A + A... A for the semi-circle cm A mm d) Using A πr and π 3.4, find the area of the shaded shape. c) Using A πr and π 3.4, find the area of the semi-circle. cm A... cm A... A... A cm page 8 Math s Mate Blue/Green Skill Builder 8

18 Skill 8. Calculating the volume of any prism. Use the general formula. prism h MMBlue MMGreen V of base height of prism Bh B Q. Using V Bh find the volume of the prism. A. A Bh where B 50 and h mm 3 B 50 mm 0 mm a) Using V Bh find the volume of the triangular prism. b) Using Volume area of the base height of the prism, find the volume of the pentagonal prism. h 0 mm 5 mm 0 mm h cm B B 8. V 50 0 c) Using V Bh find the volume of the hexagonal prism. mm 3 V d) Using V Bh find the volume of the prism. B 7 ft h 8 ft B 660 mm 5 mm V e) Using V Bh find the volume of the triangular prism.. B... V h ft 3 mm 3 V f) Using V Bh find the volume of the triangular prism. 30 mm 60 mm 0 mm B... mm 3 V page 8 Math s Mate Blue/Green Skill Builder 8

Area. Area Overview. Define: Area:

Area. Area Overview. Define: Area: Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.

More information

Area of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in

Area of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in

More information

Area of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:

Area of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams: Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of

More information

Solids. Objective A: Volume of a Solids

Solids. Objective A: Volume of a Solids Solids Math00 Objective A: Volume of a Solids Geometric solids are figures in space. Five common geometric solids are the rectangular solid, the sphere, the cylinder, the cone and the pyramid. A rectangular

More information

Calculating Area, Perimeter and Volume

Calculating Area, Perimeter and Volume Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly

More information

Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area of Parallelograms, Triangles, and Trapezoids (pages 314 318) Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base

More information

Area of Parallelograms (pages 546 549)

Area of Parallelograms (pages 546 549) A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

More information

VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:

More information

1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?

1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack? Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is

More information

Surface Area Quick Review: CH 5

Surface Area Quick Review: CH 5 I hope you had an exceptional Christmas Break.. Now it's time to learn some more math!! :) Surface Area Quick Review: CH 5 Find the surface area of each of these shapes: 8 cm 12 cm 4cm 11 cm 7 cm Find

More information

9 Area, Perimeter and Volume

9 Area, Perimeter and Volume 9 Area, Perimeter and Volume 9.1 2-D Shapes The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right

More information

Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min. Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles

More information

Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.

Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square. Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional

More information

Circumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice.

Circumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice. Name: Period GPreAP UNIT 14: PERIMETER AND AREA I can define, identify and illustrate the following terms: Perimeter Area Base Height Diameter Radius Circumference Pi Regular polygon Apothem Composite

More information

Perimeter is the length of the boundary of a two dimensional figure.

Perimeter is the length of the boundary of a two dimensional figure. Section 2.2: Perimeter and Area Perimeter is the length of the boundary of a two dimensional figure. The perimeter of a circle is called the circumference. The perimeter of any two dimensional figure whose

More information

YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!

YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR! DETAILED SOLUTIONS AND CONCEPTS - SIMPLE GEOMETRIC FIGURES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST

More information

43 Perimeter and Area

43 Perimeter and Area 43 Perimeter and Area Perimeters of figures are encountered in real life situations. For example, one might want to know what length of fence will enclose a rectangular field. In this section we will study

More information

Basic Math for the Small Public Water Systems Operator

Basic Math for the Small Public Water Systems Operator Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg Introduction Area In this module we will learn how to calculate the

More information

GAP CLOSING. 2D Measurement. Intermediate / Senior Student Book

GAP CLOSING. 2D Measurement. Intermediate / Senior Student Book GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2-D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas

More information

Finding Volume of Rectangular Prisms

Finding Volume of Rectangular Prisms MA.FL.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of three-dimensional composite shapes.

More information

GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book

GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book GAP CLOSING Volume and Surface Area Intermediate / Senior Student Book Volume and Surface Area Diagnostic...3 Volumes of Prisms...6 Volumes of Cylinders...13 Surface Areas of Prisms and Cylinders...18

More information

B = 1 14 12 = 84 in2. Since h = 20 in then the total volume is. V = 84 20 = 1680 in 3

B = 1 14 12 = 84 in2. Since h = 20 in then the total volume is. V = 84 20 = 1680 in 3 45 Volume Surface area measures the area of the two-dimensional boundary of a threedimensional figure; it is the area of the outside surface of a solid. Volume, on the other hand, is a measure of the space

More information

Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees

Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Apex in a pyramid or cone, the vertex opposite the base; in

More information

Characteristics of the Four Main Geometrical Figures

Characteristics of the Four Main Geometrical Figures Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.

More information

MENSURATION. Definition

MENSURATION. Definition MENSURATION Definition 1. Mensuration : It is a branch of mathematics which deals with the lengths of lines, areas of surfaces and volumes of solids. 2. Plane Mensuration : It deals with the sides, perimeters

More information

Area is a measure of how much space is occupied by a figure. 1cm 1cm

Area is a measure of how much space is occupied by a figure. 1cm 1cm Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number

More information

SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid

SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.

More information

MATH STUDENT BOOK. 6th Grade Unit 8

MATH STUDENT BOOK. 6th Grade Unit 8 MATH STUDENT BOOK 6th Grade Unit 8 Unit 8 Geometry and Measurement MATH 608 Geometry and Measurement INTRODUCTION 3 1. PLANE FIGURES 5 PERIMETER 5 AREA OF PARALLELOGRAMS 11 AREA OF TRIANGLES 17 AREA OF

More information

Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?

Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane

More information

Perimeter, Area, and Volume

Perimeter, Area, and Volume Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all

More information

CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.

CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder. TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has

More information

Estimating Angle Measures

Estimating Angle Measures 1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle

More information

Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.

Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same. Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length

More information

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby

More information

Geometry - Calculating Area and Perimeter

Geometry - Calculating Area and Perimeter Geometry - Calculating Area and Perimeter In order to complete any of mechanical trades assessments, you will need to memorize certain formulas. These are listed below: (The formulas for circle geometry

More information

Algebra Geometry Glossary. 90 angle

Algebra Geometry Glossary. 90 angle lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

More information

Lateral and Surface Area of Right Prisms

Lateral and Surface Area of Right Prisms CHAPTER A Lateral and Surface Area of Right Prisms c GOAL Calculate lateral area and surface area of right prisms. You will need a ruler a calculator Learn about the Math A prism is a polyhedron (solid

More information

Chapter 8 Geometry We will discuss following concepts in this chapter.

Chapter 8 Geometry We will discuss following concepts in this chapter. Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles

More information

SURFACE AREA AND VOLUME

SURFACE AREA AND VOLUME SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has

More information

Geometry Notes VOLUME AND SURFACE AREA

Geometry Notes VOLUME AND SURFACE AREA Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate

More information

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

More information

Shape Dictionary YR to Y6

Shape Dictionary YR to Y6 Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use

More information

MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.

MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile. MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units

More information

Geometry Unit 6 Areas and Perimeters

Geometry Unit 6 Areas and Perimeters Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose

More information

12 Surface Area and Volume

12 Surface Area and Volume 12 Surface Area and Volume 12.1 Three-Dimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids

More information

10-3 Area of Parallelograms

10-3 Area of Parallelograms 0-3 Area of Parallelograms MAIN IDEA Find the areas of parallelograms. NYS Core Curriculum 6.A.6 Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest,

More information

Geometry Notes PERIMETER AND AREA

Geometry Notes PERIMETER AND AREA Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

More information

Unit 5 Area. What Is Area?

Unit 5 Area. What Is Area? Trainer/Instructor Notes: Area What Is Area? Unit 5 Area What Is Area? Overview: Objective: Participants determine the area of a rectangle by counting the number of square units needed to cover the region.

More information

Platonic Solids. Some solids have curved surfaces or a mix of curved and flat surfaces (so they aren't polyhedra). Examples:

Platonic Solids. Some solids have curved surfaces or a mix of curved and flat surfaces (so they aren't polyhedra). Examples: Solid Geometry Solid Geometry is the geometry of three-dimensional space, the kind of space we live in. Three Dimensions It is called three-dimensional or 3D because there are three dimensions: width,

More information

G3-33 Building Pyramids

G3-33 Building Pyramids G3-33 Building Pyramids Goal: Students will build skeletons of pyramids and describe properties of pyramids. Prior Knowledge Required: Polygons: triangles, quadrilaterals, pentagons, hexagons Vocabulary:

More information

Area of Circles. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and record in the blanks above.

Area of Circles. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and record in the blanks above. Name: Area of Circles Label: Length: Label: Length: A Part 1 1. Label the diameter and radius of Circle A. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and recd

More information

12-1 Representations of Three-Dimensional Figures

12-1 Representations of Three-Dimensional Figures Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular

More information

Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)

Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes) Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.

More information

PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.

PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the

More information

Grade 8 Mathematics Geometry: Lesson 2

Grade 8 Mathematics Geometry: Lesson 2 Grade 8 Mathematics Geometry: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside

More information

Pizza! Pizza! Assessment

Pizza! Pizza! Assessment Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the

More information

Target To know the properties of a rectangle

Target To know the properties of a rectangle Target To know the properties of a rectangle (1) A rectangle is a 3-D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles

More information

Think About This Situation

Think About This Situation Think About This Situation A popular game held at fairs or parties is the jelly bean guessing contest. Someone fills a jar or other large transparent container with a known quantity of jelly beans and

More information

Angles that are between parallel lines, but on opposite sides of a transversal.

Angles that are between parallel lines, but on opposite sides of a transversal. GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,

More information

39 Symmetry of Plane Figures

39 Symmetry of Plane Figures 39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that

More information

Perimeter. 14ft. 5ft. 11ft.

Perimeter. 14ft. 5ft. 11ft. Perimeter The perimeter of a geometric figure is the distance around the figure. The perimeter could be thought of as walking around the figure while keeping track of the distance traveled. To determine

More information

Scale Factors and Volume. Discovering the effect on the volume of a prism when its dimensions are multiplied by a scale factor

Scale Factors and Volume. Discovering the effect on the volume of a prism when its dimensions are multiplied by a scale factor Scale Factors and Discovering the effect on the volume of a prism when its dimensions are multiplied by a scale factor Find the volume of each prism 1. 2. 15cm 14m 11m 24m 38cm 9cm V = 1,848m 3 V = 5,130cm

More information

2nd Semester Geometry Final Exam Review

2nd Semester Geometry Final Exam Review Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular

More information

Filling and Wrapping: Homework Examples from ACE

Filling and Wrapping: Homework Examples from ACE Filling and Wrapping: Homework Examples from ACE Investigation 1: Building Smart Boxes: Rectangular Prisms, ACE #3 Investigation 2: Polygonal Prisms, ACE #12 Investigation 3: Area and Circumference of

More information

GAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement

GAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement GAP CLOSING 2D Measurement GAP CLOSING 2D Measurement Intermeditate / Senior Facilitator s Guide 2-D Measurement Diagnostic...4 Administer the diagnostic...4 Using diagnostic results to personalize interventions...4

More information

MCA Formula Review Packet

MCA Formula Review Packet MCA Formula Review Packet 1 3 4 5 6 7 The MCA-II / BHS Math Plan Page 1 of 15 Copyright 005 by Claude Paradis 8 9 10 1 11 13 14 15 16 17 18 19 0 1 3 4 5 6 7 30 8 9 The MCA-II / BHS Math Plan Page of 15

More information

Conjectures for Geometry for Math 70 By I. L. Tse

Conjectures for Geometry for Math 70 By I. L. Tse Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:

More information

WEIGHTS AND MEASURES. Linear Measure. 1 Foot12 inches. 1 Yard 3 feet - 36 inches. 1 Rod 5 1/2 yards - 16 1/2 feet

WEIGHTS AND MEASURES. Linear Measure. 1 Foot12 inches. 1 Yard 3 feet - 36 inches. 1 Rod 5 1/2 yards - 16 1/2 feet WEIGHTS AND MEASURES Linear Measure 1 Foot12 inches 1 Yard 3 feet - 36 inches 1 Rod 5 1/2 yards - 16 1/2 feet 1 Furlong 40 rods - 220 yards - 660 feet 1 Mile 8 furlongs - 320 rods - 1,760 yards 5,280 feet

More information

CSU Fresno Problem Solving Session. Geometry, 17 March 2012

CSU Fresno Problem Solving Session. Geometry, 17 March 2012 CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news

More information

By the end of this set of exercises, you should be able to:

By the end of this set of exercises, you should be able to: BASIC GEOMETRIC PROPERTIES By the end of this set of exercises, you should be able to: find the area of a simple composite shape find the volume of a cube or a cuboid find the area and circumference of

More information

UNIT H1 Angles and Symmetry Activities

UNIT H1 Angles and Symmetry Activities UNIT H1 Angles and Symmetry Activities Activities H1.1 Lines of Symmetry H1.2 Rotational and Line Symmetry H1.3 Symmetry of Regular Polygons H1.4 Interior Angles in Polygons Notes and Solutions (1 page)

More information

Quick Reference ebook

Quick Reference ebook This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

More information

Conjectures. Chapter 2. Chapter 3

Conjectures. Chapter 2. Chapter 3 Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical

More information

Geometry of 2D Shapes

Geometry of 2D Shapes Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles

More information

Parts and Wholes. In a tangram. 2 small triangles (S) cover a medium triangle (M) 2 small triangles (S) cover a square (SQ)

Parts and Wholes. In a tangram. 2 small triangles (S) cover a medium triangle (M) 2 small triangles (S) cover a square (SQ) Parts and Wholes. L P S SQ M In a tangram small triangles (S) cover a medium triangle (M) small triangles (S) cover a square (SQ) L S small triangles (S) cover a parallelogram (P) small triangles (S) cover

More information

3D shapes. Level A. 1. Which of the following is a 3-D shape? A) Cylinder B) Octagon C) Kite. 2. What is another name for 3-D shapes?

3D shapes. Level A. 1. Which of the following is a 3-D shape? A) Cylinder B) Octagon C) Kite. 2. What is another name for 3-D shapes? Level A 1. Which of the following is a 3-D shape? A) Cylinder B) Octagon C) Kite 2. What is another name for 3-D shapes? A) Polygon B) Polyhedron C) Point 3. A 3-D shape has four sides and a triangular

More information

CBA Volume: Student Sheet 1

CBA Volume: Student Sheet 1 CBA Volume: Student Sheet 1 For each problem, decide which cube building has more room inside, or if they have the same amount of room. Then find two ways to use cubes to check your answers, one way that

More information

MATHS ACTIVITIES FOR REGISTRATION TIME

MATHS ACTIVITIES FOR REGISTRATION TIME MATHS ACTIVITIES FOR REGISTRATION TIME At the beginning of the year, pair children as partners. You could match different ability children for support. Target Number Write a target number on the board.

More information

Measurement. Volume It All Stacks Up. Activity:

Measurement. Volume It All Stacks Up. Activity: Measurement Activity: TEKS: Overview: Materials: Grouping: Time: Volume It All Stacks Up (7.9) Measurement. The student solves application problems involving estimation and measurement. The student is

More information

Exercise 11.1. Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Exercise 11.1. Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area? 11 MENSURATION Exercise 11.1 Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area? (a) Side = 60 m (Given) Perimeter of

More information

What You ll Learn. Why It s Important

What You ll Learn. Why It s Important These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why

More information

CBA Fractions Student Sheet 1

CBA Fractions Student Sheet 1 Student Sheet 1 1. If 3 people share 12 cookies equally, how many cookies does each person get? 2. Four people want to share 5 cakes equally. Show how much each person gets. Student Sheet 2 1. The candy

More information

Section 7.2 Area. The Area of Rectangles and Triangles

Section 7.2 Area. The Area of Rectangles and Triangles Section 7. Area The Area of Rectangles and Triangles We encounter two dimensional objects all the time. We see objects that take on the shapes similar to squares, rectangle, trapezoids, triangles, and

More information

Math 0306 Final Exam Review

Math 0306 Final Exam Review Math 006 Final Exam Review Problem Section Answers Whole Numbers 1. According to the 1990 census, the population of Nebraska is 1,8,8, the population of Nevada is 1,01,8, the population of New Hampshire

More information

2006 Geometry Form A Page 1

2006 Geometry Form A Page 1 2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches

More information

MATH 110 Landscape Horticulture Worksheet #4

MATH 110 Landscape Horticulture Worksheet #4 MATH 110 Landscape Horticulture Worksheet #4 Ratios The math name for a fraction is ratio. It is just a comparison of one quantity with another quantity that is similar. As a Landscape Horticulturist,

More information

Area and Circumference

Area and Circumference 4.4 Area and Circumference 4.4 OBJECTIVES 1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert

More information

Applications for Triangles

Applications for Triangles Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given

More information

Similar shapes. 33.1 Similar triangles CHAPTER. Example 1

Similar shapes. 33.1 Similar triangles CHAPTER. Example 1 imilar shapes 33 HTR 33.1 imilar triangles Triangle and triangle have the same shape but not the same size. They are called similar triangles. The angles in triangle are the same as the angles in triangle,

More information

Tallahassee Community College PERIMETER

Tallahassee Community College PERIMETER Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides

More information

SOL Warm-Up Graphing Calculator Active

SOL Warm-Up Graphing Calculator Active A.2a (a) Using laws of exponents to simplify monomial expressions and ratios of monomial expressions 1. Which expression is equivalent to (5x 2 )(4x 5 )? A 9x 7 B 9x 10 C 20x 7 D 20x 10 2. Which expression

More information

Grade 3 Core Standard III Assessment

Grade 3 Core Standard III Assessment Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse

More information

16 Circles and Cylinders

16 Circles and Cylinders 16 Circles and Cylinders 16.1 Introduction to Circles In this section we consider the circle, looking at drawing circles and at the lines that split circles into different parts. A chord joins any two

More information

The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- Area = 1 2 D x d CIRCLE.

The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- Area = 1 2 D x d CIRCLE. Revision - Areas Chapter 8 Volumes The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- SQUARE RECTANGE RHOMBUS KITE B dd d D D Area = 2 Area = x B

More information

CALCULATING THE AREA OF A FLOWER BED AND CALCULATING NUMBER OF PLANTS NEEDED

CALCULATING THE AREA OF A FLOWER BED AND CALCULATING NUMBER OF PLANTS NEEDED This resource has been produced as a result of a grant awarded by LSIS. The grant was made available through the Skills for Life Support Programme in 2010. The resource has been developed by (managers

More information

Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find

More information

2014 2015 Geometry B Exam Review

2014 2015 Geometry B Exam Review Semester Eam Review 014 015 Geometr B Eam Review Notes to the student: This review prepares ou for the semester B Geometr Eam. The eam will cover units 3, 4, and 5 of the Geometr curriculum. The eam consists

More information

Dŵr y Felin Comprehensive School. Perimeter, Area and Volume Methodology Booklet

Dŵr y Felin Comprehensive School. Perimeter, Area and Volume Methodology Booklet Dŵr y Felin Comprehensive School Perimeter, Area and Volume Methodology Booklet Perimeter, Area & Volume Perimeters, Area & Volume are key concepts within the Shape & Space aspect of Mathematics. Pupils

More information

Year 9 mathematics test

Year 9 mathematics test Ma KEY STAGE 3 Year 9 mathematics test Tier 6 8 Paper 1 Calculator not allowed First name Last name Class Date Please read this page, but do not open your booklet until your teacher tells you to start.

More information

Assessment For The California Mathematics Standards Grade 4

Assessment For The California Mathematics Standards Grade 4 Introduction: Summary of Goals GRADE FOUR By the end of grade four, students understand large numbers and addition, subtraction, multiplication, and division of whole numbers. They describe and compare

More information