# 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:

Size: px
Start display at page:

Download "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:"

Transcription

1 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 each triangle in 11in 12in 9in 21in 14in 19in 13in 1 1 Area of a trapezoid: The area of a triangle can be found with the following formula: A 1 2 h( b 1 b 2 ) or A h b 1 b 2 ( 2 ) h b 2 b 1 Solve: Find the area of each trapezoid. 3in in 9in 12in 12in 14in 9in 17in

2 Area Review Area of a circle: The area of a circle can be found with the following formula: Circumference of a circle looks similar: Area and circumference of a circle: Find the area and circumference of each: C 2 r or C 2 A r d 1 32in Combinations: Find the area and perimeter of each: in 1 Review: Find the area and perimeter/circumference of each: in 2 9in 1 12in 2 20in

3 Area Practice Find the area of each: For #7-12 find the circumference/perimeter. ROUND TO THE TENTH WHERE APPLICABLE in 24in 7in 13in 12in 1 14in 2 14in in in 13in 3in 11in 7in 11in 4in in 18n 30in 7. A: C: 8. A: C: 9. A: C: in 7in 11.3in 11in 10. A: P: 11. A: P: 12. A: P:

4 Area of Regular Polygons What formula could be used to determine the area (A) of a regular polygon given the: Number of sides: n Side length: s Apothem (inradius): a A 1 2 asn a s This is easiest to think about as finding the area of n triangles with base s and height a. The area of the pentagon to the right is: A cm 2 10cm How can this formula be simplified given the perimeter P of the polygon? 2 14cm Find the area of each regular polygon below: Round to the tenth. 1. A nonagon (9 sides) whose side length is 12cm and whose apothem is 16.5cm? 2. A hexagon whose sides measure 6 inches and whose apothem is 5.2 inches. 3. An octagon whose sides measure 61 inches and whose apothem is 74 inches. 4. A heptagon whose apothem measure inches and whose sides are 10 inches long. 5. A polygon whose perimeter is 60 inches and whose apothem is 8.5 in?

5 Area of Regular Polygons Determine the area of each figure below: cm 6 cm 5 cm 4 cm What is the perimeter of each figure below? (round to the tenth) 8. Area = 585cm 2 9. Area = 364 in 2 13 cm 10.4 in What is the apothem of each regular polygon below? (round to the tenth) 10. Area = 121 cm Area = 1075 ft 2 5 cm 25 feet

6 Area of Regular Polygons Determine the area of each regular polygon below: cm 9 cm 5 cm 6 cm cm 52cm 8.5 ft 13 ft Given the area, what is the side length of each figure below? (round to the tenth) 5. Area = 120.7in 2 6. Area = 5 2 6cm 4.2 in 5. 6.

7 Polygon Area: Determine the area of each shaded area below: (to the tenth) (all polygons shown are regular) cm 17 feet 2.2cm 2.2cm 14 feet Find the area of the shaded region below: Round to the tenth. 8m 8.2m Challenge: Find the area of the shaded region below: Round to the tenth. 12ft 10.

8 Surface Area Surface Area is the sum of the areas of all faces which enclose a solid. You should alreay be able to find the surface area of basic solids like those below: 4ft 5ft Be methodical! Two ends: 4 x 5 x 2 = 40ft 2 Front and back: 10 x 5 x 2 = 100ft 2 Top and bottom: 10 x 4 x 2 = 80ft 2 10ft Surface area = = 220ft 2 9in 20in Top and bottom = 2(3.14 x 9 2 ) = (remember the formula for area of a circle is Rectangular wrap = 2 x 3.14 x 9 x 20 = in 2 (remember the formula for area of a the wrap is Total surface area: r 2 ( 2 r)h Prisms have identical bases connected by parallelograms (generally rectangles). To find the surface area of a prism, simply add the area of the bases to the area of the lateral faces (sides). Example: (pentagon is regular) 8cm Be methodical! The pentagons are regular: Each pentagon: A = 1/2 x 7 x 10 x 5 = 175cm 2 times 2 = 350 cm 2 7cm 10cm Five lateral faces: A = 8 x 10 = 80 cm 2 times 5 = 400 cm 2 Total surface area = = 750cm 2 Review practice: 1. What is the surface area of a 3-inch tall cylinder with a 7-inch radius? 2. What is the surface area of a 9-foot tall prism whose bases are regular hexagons. Each hexagon has 12-foot sides and a 10-foot apothem.

9 31cm Surface Area Determine the surface area of each solid below: Round all answers to the hundredth. Work on a separate sheet. 3ft 100cm 15ft 3ft 7in 30cm 3. A = 4. A = 5. A = octagon apothem = 12 inches circle diameter = 2ft 9in 3ft 3ft 3ft 6. A = 7. A = 3m Circle radius: 12ft Pentagon sides: 3ft Pentagon apothem: 2ft 20m 10ft 8. A = 9. A =

10 10m 16.5 cm Surface Area: Find the surface area of each: 12m There are 5 surfaces. 9m 30cm There are 9 surfaces. 16cm 10ft 8ft There are 7 surfaces. 15ft cylinder diameter = 18ft diameter = 4ft There are 7 surfaces. 10m 6m

11 31cm Prism/Cylinder Volume The formula used to find the volume of a prism or cylinder: V Bh Where B is the area of the base and h is the height. This applies whether the figure is right or oblique (Oblique means slanted. Height is measured along the altitude). Practice: Find the volume of each solid. Round to the tenth. 1. (pentagon is regular) 2. 7m 6cm 6m 7cm 10cm cm 12m 13m 5m 10cm 7m circle diameter = 4ft 100cm 30cm 6ft 6ft 6ft 5. 6.

12 Pyramid/Cone Volume The formula used to find the volume of a pyramid or cone: V 1 3 Bh Where B is the area of the base and h is the height. This applies whether the figure is right or oblique (height is measured along the altitude). Practice: Find the volume of each solid. 7. (square-based pyramid) 8. (triangle-based pyramid) ft 10ft 3in 6ft 8ft 10ft 4in 12ft

13 Volume Practice Determine the volume of each solid below: Round all answers to the hundredth. Work on a separate sheet. 15ft 4ft 4ft 3in 4in 8m 15m 17m 1.V = 2. V = 3. V = 4. V = 5. V = 6ft 5ft 5ft 3ft 15ft 5ft 6ft cylinder diameter = 10ft 6. V = 7. V =

14 Review Determine the area of each: Round to the tenth in 40in 50in 20in Determine the area of each: Round to the tenth cm 3.4cm 9cm 21in 5cm 20in Determine the surface area of each: Round to the tenth ft 5ft 7in 11in 7cm 11cm 10cm 10ft cylinder diameter = 12ft Determine the volume of each: Round to the tenth diameter = 4m 9in 17in 1 12in 18m 24m 30m 10m 10m 6m

15 Surface Area and Volume Determine the surface area and volume for each: 3in 7in 11in 4in 4in 9in 1. A = 2. A = 3. A = V = V = V = 11cm 9in 7cm 10cm Small Circle Radius: 4in Large Circle Radius: 4. A = 5. A = V = V = 3in (cylinder with a cone-shaped hole) 3in 4in 6. A = 7. V = V = (no surface area on this one)

16 Surface Area and Volume Determine the surface area and volume for each: diameter = 4ft 13in 7in 10m 12in 17in 10m 6m 1. A = 2. A = 3. A = V = V = V = Surface Area and Volume Determine the surface area and volume for each: diameter = 4ft 13in 7in 10m 12in 17in 10m 6m 1. A = 2. A = 3. A = V = V = V =

17 Changing Dimensions Changing the dimensions of an object effects the area and volume. Here are some easy examples: Ex: A square is enlarged so that the length of each side is doubled. If the area of the original square was 7 square inches, what will be the area of the enlarged square? 2x2=4 times bigger. Ex: A cube has one-inch edges. How many times larger is the volume of a cube with edges that are three times longer? 3x3x3=27 times bigger. If you increase the dimensions of an object, the volume increases by the product of those increases. Example: The volume of a rectangular prism is 3. You double the length, width, and height. What will the new volume be? Practice: 1. The area of a reactangle is 15cm 2. If you triple the length and double the width, what will the area of the new rectangle be? 2. A cube has a volume of 2cm 3. Will a cube that has 8 times more volume be twice as tall, three times as tall, 4 times as tall, or 8 times as tall? 3. What happens to the area of a circle when you triple its radius?

18 Changing Dimensions Practice: Solve each. 1. A rectangular prism is 3x4x5 inches. How many times greater is the volume of a 6x8x15 rectangular prism? (If you are not sure, find each volume and divide). 2. When the sides of a triangle are 6 inches long, the area of the triangle is about 15.6 square inches. What would be the area of an equilateral triangle whose sides are 2 inches long? (round to the tenth) 3. A large circle has 81 times the area of a small circle. If the radius of the large circle is 45 inches, what is the radius of the small circle? Practice: Solve each. 1. The radius and height of a cone are tripled. What effect does this have on the cone s volume? 2. The radius of a cylinder is doubled, but the height is not changed. If the original cylinder had a volume of 4cm 3, what is the volume of the new cylinder? 3. A cylinder and a cone have the same base and equal volumes. If the cylinder is 15 inches tall, how tall is the cone? Practice: Solve each. 1. The length and width of a rectangular pyramid are tripled, and the height is doubled. How many times larger is the new pyramid than the original? 2. The dimensions of a cube are increased by 50% (1.5 times). If the original cube had a volume of 1 3, what is the volume of the new cube? 3. You have a square sheet of construction paper. You want a sheet that has twice the area. How many times wider will the new sheet be?

19 Changing Dimensions Complete the following area problems: in 1 30in 4in 24in in 1 Leave answers below in terms of Pi in 30in Complete the following area problems: 10. What happens to the area of a square when you: a. Double the sides. b. Triple the sides. c. Halve the sides. 11. What happens to the volume of a cylinder when you: a. Double the radius only. b. Triple the height only. c. Double the radius and triple the height. 12. A rectangle has an area of 12cm 2. What will the area be if you: a. Triple all sides. b. Multiply all sides by 1.5.

20 Changing Dimensions Practice: Solve each. 13. A rectangular prism is 2x4x7 inches. How many times greater is the volume of a 6x8x7 rectangular prism? (If you are not sure, find each volume and divide). 14. When the sides of a pentagon are 6 inches long, the area of the pentagon is about 63 square inches. What would the area of a pentagon whose sides are 2 inches long? 15. A large circle has 36 times the area of a small circle. If the radius of the large circle is 24 inches, what is the radius of the small circle? 16. The radius and height of a cylinder are tripled. What effect does this have on the volume? 17. The radius of a cylinder is doubled, and the height is multiplied by 5. If the original cylinder had a volume of 10cm 3, what is the volume of the new cylinder? 18. A right triangle has an area of 2. If all the dimensions are multiplied by 4, what will the area of the new triangle be? 19. The length and width of a rectangular pyramid are doubled, and the height is tripled. How many times larger is the new pyramid than the original? 20. The dimensions of a cube are increased so that they are 2.5 times longer. If the original cube had a volume of 3, what is the volume of the new cube?

21 Changing Dimensions Practice: Solve each. 1. The area of a circle is 30in 2. If you triple the circle s radius, what will its new area be? 2. When a hexagon has 2-inch sides, its area is about 10.4in 2. What will be the approximate area of a hexagon whose sides are 10 inches long?? 3. A rectangular prism has a volume of 17cm 2. If you double the length and width, but leave the height unchanged, what will be the volume of the new prism? 4. If you want to double the area of a square, by what percent should you increase the length of its sides. hint: Try using a 10-inch square, double its area, and find the length of the sides of the new square. 5. The volume of the regular dodecahedron below with an edge length of 4-inches is about 490 in 3. What would be the volume of a regular dodecahedron whose edges are a foot long? 6. The volume of a cone is 3in 3. What would be the volume after each modification below? (each part refers to the original figure). a. Double the radius only. b. Triple the height only. c. Double the height and triple the radius. d. Increase the height and radius by 50%. 7. If you want to double the volume of a cube, by what percent should you increase the edge length? a.20% b.23% c.26% d.30% e.40%

22 Area and Volume Practice Test Determine the area of each figure below. Round to the tenth. Figures not to scale in 12in 4in 13in 9in cm 7in Determine the volume for each figure below: (figures not to scale, round to the tenth) 12m 9m 15m 17m 8m 5. Volume = 6. Volume =

23 Area and Volume Practice Test Determine the surface area for each figure below: (figures not to scale, round to the tenth) 7in diameter = 5ft 13in 9in 12in 13in 12m 17in 12m 7m 7. Surface Area = 8. Surface Area = Solve each problem involving changing dimensions: 9. A rectangular prism has a volume of 5cm 3. If you triple the length, width, and height, what will the volume of the enlarged prism be? When the radius of a circle is multipled by 4, the area of the new circle is 40 in 3. What was the area of the original circle? The volume of a rectangular pyramid is 7m 3. What is the volume of a pyramid that is twice as tall, three times as long, and four times as wide? A cube has edges that are 6 centimeters long. How many times greater is the volume of a cube with 9 centimeter sides? Pledge and sign: 12.

### 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

### 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

### 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.

### 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:

### 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

### 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

### 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

### 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

### 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.

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Geometry Final Exam Review Worksheet

Geometry Final xam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. (2) Given the figure to the right, is tangent at, sides as marked, find the values of x, y, and z please.

### 12 Surface Area and Volume

CHAPTER 12 Surface Area and Volume Chapter Outline 12.1 EXPLORING SOLIDS 12.2 SURFACE AREA OF PRISMS AND CYLINDERS 12.3 SURFACE AREA OF PYRAMIDS AND CONES 12.4 VOLUME OF PRISMS AND CYLINDERS 12.5 VOLUME

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.

Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.

### 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

### 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.

### 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

### 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

### 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.

### 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

### 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

### 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

### Area, Perimeter, Volume and Pythagorean Theorem Assessment

Area, Perimeter, Volume and Pythagorean Theorem Assessment Name: 1. Find the perimeter of a right triangle with legs measuring 10 inches and 24 inches a. 34 inches b. 60 inches c. 120 inches d. 240 inches

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### The GED math test gives you a page of math formulas that

Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding

### 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

### 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

### 56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.

6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which

### Chapter 4: Area, Perimeter, and Volume. Geometry Assessments

Chapter 4: Area, Perimeter, and Volume Geometry Assessments Area, Perimeter, and Volume Introduction The performance tasks in this chapter focus on applying the properties of triangles and polygons to

### 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

### 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

### 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

### 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

### 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

### ACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone.

8. Volumes of Cones How can you find the volume of a cone? You already know how the volume of a pyramid relates to the volume of a prism. In this activity, you will discover how the volume of a cone relates

### 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

### 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,

### 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.

### 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

### 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

### 2. Complete the table to identify the effect tripling the radius of a cylinder s base has on its volume. Cylinder Height (cm) h

Name: Period: Date: K. Williams ID: A 8th Grade Chapter 14 TEST REVIEW 1. Determine the volume of the cylinder. Use 3.14 for. 2. Complete the table to identify the effect tripling the radius of a cylinder

### 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

### 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

### Area & Volume. 1. Surface Area to Volume Ratio

1 1. Surface Area to Volume Ratio Area & Volume For most cells, passage of all materials gases, food molecules, water, waste products, etc. in and out of the cell must occur through the plasma membrane.

### 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:

### 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

### 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

### Session 8 Volume. cone cross section cylinder net prism sphere

Key Terms in This Session Previously Introduced volume Session 8 Volume New in This Session cone cross section cylinder net prism sphere Introduction Volume is literally the amount of space filled. But

### Lesson 9.1 The Theorem of Pythagoras

Lesson 9.1 The Theorem of Pythagoras Give all answers rounded to the nearest 0.1 unit. 1. a. p. a 75 cm 14 cm p 6 7 cm 8 cm 1 cm 4 6 4. rea 9 in 5. Find the area. 6. Find the coordinates of h and the radius

### Section 7.1 Solving Right Triangles

Section 7.1 Solving Right Triangles Note that a calculator will be needed for most of the problems we will do in class. Test problems will involve angles for which no calculator is needed (e.g., 30, 45,

### 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

### 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

### 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,

### 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

### MATH 100 PRACTICE FINAL EXAM

MATH 100 PRACTICE FINAL EXAM Lecture Version Name: ID Number: Instructor: Section: Do not open this booklet until told to do so! On the separate answer sheet, fill in your name and identification number

### 1-6 Two-Dimensional Figures. Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Stop signs are constructed in the shape of a polygon with 8 sides of equal length The polygon has 8 sides A polygon with 8 sides is an octagon All sides of the polygon are congruent and all angles are

### 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:

### 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

### 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

### Geometry and Measurement

The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

### GCSE Exam Questions on Volume Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice.

Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice. Cylindrical glasses of height 10 cm and radius 3 cm are to be filled from the carton. How

### 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

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

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

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

### 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)

### Lesson 24: Surface Area

Student Outcomes Students determine the surface area of three-dimensional figures, those that are composite figures and those that have missing sections. Lesson Notes This lesson is a continuation of Lesson

### PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY

PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY The Student Handout is page 11. Give this page to students as a separate sheet. Area of Circles and Squares Circumference and Perimeters Volume of Cylinders

### 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

### 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

### How To Find The Area Of A Shape

9 Areas and Perimeters This is is our next key Geometry unit. In it we will recap some of the concepts we have met before. We will also begin to develop a more algebraic approach to finding areas and perimeters.

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Santa Monica College COMPASS Geometry Sample Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area of the shaded region. 1) 5 yd 6 yd

### Keystone National High School Placement Exam Math Level 1. Find the seventh term in the following sequence: 2, 6, 18, 54

1. Find the seventh term in the following sequence: 2, 6, 18, 54 2. Write a numerical expression for the verbal phrase. sixteen minus twelve divided by six Answer: b) 1458 Answer: d) 16 12 6 3. Evaluate

### 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

### MATHEMATICS FOR ENGINEERING BASIC ALGEBRA

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL 4 AREAS AND VOLUMES This is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves on fundamentals.