9-3. Area of Irregular Figures Going Deeper EXPLORE. Essential question: How do you find the area of composite figures? Area of a Composite Figure

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "9-3. Area of Irregular Figures Going Deeper EXPLORE. Essential question: How do you find the area of composite figures? Area of a Composite Figure"

Transcription

1 Name Class Date Area of Irregular Figures Going Deeper Essential question: How do you find the area of composite figures? CC.7.G.6 EXPLORE Area of a Composite Figure video tutor Aaron was plotting the shape of his garden on grid paper. While it was an irregular shape, it was perfect for his yard. Each square on the grid represents 1 square meter. A Describe one way you can find the area of this garden. B The area of the garden is square meters. C Compare your results with other students. What other methods were used to find the area? D How does your area compare with the area found using different methods? REFLECT 1. Use dotted lines to show two different ways Aaron s garden could be divided up into simple geometric figures. Chapter Lesson 3

2 A composite figure is made up of simple geometric shapes. To find the area of composite figures and other irregular shaped figures, divide it into simple, non-overlapping figures. Find the area of each simpler figure, and then add them together to find the total area of the composite figure. Use the chart below to review some common area formulas. Shape triangle square rectangle parallelogram trapezoid Area Formula 2 bh s 2 lw bh 2 h( b 1 + b 2 ) 2 CC.7.G.6 EXAMPLE Finding the Area of a Composite Figure Find the area of the figure. A Into what two figures can you divide this composite figure? 3 cm 4 cm 10 cm 2 cm 7 cm B Find the area of each shape. Area of the Parallelogram Area of the Trapezoid 10 cm 3 cm 4 cm The base of the parallelogram is The height of the parallelogram is Use the formula. bh cm. cm. The area of the parallelogram is cm 2. 7 cm The bottom base of the trapezoid is cm. 2 cm The top base the trapezoid is cm, since it is the same length as the base of the parallelogram. The height of the trapezoid is cm. Use the formula. 2 h( b 1 + b 2 ) 2 ( + ) 2 ( ) The area of the trapezoid is cm 2. Chapter Lesson 3

3 C Find the area of the composite figure. + = Area of parallelogram Area of trapezoid Area of composite shape REFLECT 2a. Describe another way to divide the shape into simpler figures. 2b. If you divide the composite figure into different shapes, what is the area? What does this tell you? 3 CC.7.G.6 example Calculating Cost Based on Area A banquet room is being carpeted. A floor plan of the room is shown at right. Each unit length represents 1 yard. Carpet costs $23.50 per square yard. How much will it cost to carpet the room? A Divide the figure into simpler shapes: a parallelogram, a rectangle, and a triangle. Show the divisions on the floor plan with dotted lines. Count the units to find the dimensions. B Find the area of the parallelogram. bh square yards D Find the area of the triangle. 2 bh 2 square yard E The area of the composite figure is yd 2. C Find the area of the rectangle. lw square yards F To calculate the cost to carpet the room, multiply by the. The cost to carpet the banquet room is. Chapter Lesson 3

4 REFLECT 3. Describe how you can estimate the cost to carpet the room. practice Find the area of each figure. Use 3.14 for π cm 5 cm 4 cm 6 m 6 cm 6 cm 4. Show two different ways to divide the composite figure. Find the area both ways. Show your work below. 12 cm 9 cm 5. Sal is tiling his entryway. The floor plan is drawn on a unit grid. Each unit length represents 1 foot. Tile costs $2.25 per square foot. How much will Sal pay to tile his entryway? 9 cm 8 cm 20 cm 18 cm 6. Reasoning A composite figure is formed by combining a square and a triangle. Its total area is 32.5 ft 2. The area of the triangle is 7.5 ft 2. What is the length of each side of the square? Chapter Lesson 3

5 Name Class Date 9-3 Additional Practice Estimate the area of each figure. Each square represents 1 square foot. Choose the letter for the best answer A 10 ft 2 C 14 ft 2 B 11 ft 2 D 15 ft 2 F 24 ft 2 H 32 ft 2 G 27 ft 2 J 36 ft 2 Find the area of each figure. Use 3.14 for The figure shows the dimensions of a room. How much carpet is needed to cover the floor? Chapter Practice and Problem Solving

6 Problem Solving Write the correct answer. 1. Explain how to find the area of the composite figure below. Then find the area. 2. Mr. Bemis carpets the living room shown below. If he pays $20 per square meter, what is the total cost of the carpet? 3. A figure is made of a square and a semi-circle. The square has sides of 16 cm each. One side of the square is also the diameter of the semi-circle. What is the total area of the figure? Use 3.14 for. 4. A figure is made of a rectangle and an isosceles right triangle. The rectangle has sides of 6 in. and 3 in. One of the short sides of the rectangle is also one of the legs of the right triangle. What is the total area of the figure? Choose the letter of the correct answer. 5. Norene builds the deck at the right. The area of the deck is 10 m 2 greater than was originally planned. What is the area of the deck? A 110 m 2 C 66 m 2 B 76 m 2 D 56 m 2 6. The grid to the right shows a swimming pool. Each square represents 1 square meter. What is the best estimate of the area of the swimming pool? F 45 m 2 H 37 m 2 G 41 m 2 J 32 m 2 Chapter Practice and Problem Solving

Name: Class: Date: Geometry Chapter 3 Review

Name: Class: Date: Geometry Chapter 3 Review Name: Class: Date: ID: A Geometry Chapter 3 Review. 1. The area of a rectangular field is 6800 square meters. If the width of the field is 80 meters, what is the perimeter of the field? Draw a diagram

More information

Area Long-Term Memory Review Review 1

Area Long-Term Memory Review Review 1 Review 1 1. To find the perimeter of any shape you all sides of the shape.. To find the area of a square, you the length and width. 4. What best identifies the following shape. Find the area and perimeter

More information

Area and Perimeter. Practice: Find the perimeter of each. Square with side length of 6 cm. Rectangle with side lengths of 4 cm and 7 cm

Area and Perimeter. Practice: Find the perimeter of each. Square with side length of 6 cm. Rectangle with side lengths of 4 cm and 7 cm Area and Perimeter Perimeter: add up all the sides (the outside of the polygon) Practice: Find the perimeter of each Square with side length of 6 cm Rectangle with side lengths of 4 cm and 7 cm Parallelogram

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

Sect 8.3 Quadrilaterals, Perimeter, and Area

Sect 8.3 Quadrilaterals, Perimeter, and Area 186 Sect 8.3 Quadrilaterals, Perimeter, and Area Objective a: Quadrilaterals Parallelogram Rectangle Square Rhombus Trapezoid A B E F I J M N Q R C D AB CD AC BD AB = CD AC = BD m A = m D m B = m C G H

More information

5 th Grade Mathematics

5 th Grade Mathematics 5 th Grade Mathematics Instructional Week 20 Rectilinear area with fractional side lengths and real-world problems involving area and perimeter of 2-dimensional shapes Paced Standards: 5.M.2: Find the

More information

Sect 9.5 - Perimeters and Areas of Polygons

Sect 9.5 - Perimeters and Areas of Polygons Sect 9.5 - Perimeters and Areas of Polygons Ojective a: Understanding Perimeters of Polygons. The Perimeter is the length around the outside of a closed two - dimensional figure. For a polygon, the perimeter

More information

Study Guide. 6.g.1 Find the area of triangles, quadrilaterals, and other polygons. Note: Figure is not drawn to scale.

Study Guide. 6.g.1 Find the area of triangles, quadrilaterals, and other polygons. Note: Figure is not drawn to scale. Study Guide Name Test date 6.g.1 Find the area of triangles, quadrilaterals, and other polygons. 1. Note: Figure is not drawn to scale. If x = 14 units and h = 6 units, then what is the area of the triangle

More information

CALCULATING PERIMETER. WHAT IS PERIMETER? Perimeter is the total length or distance around a figure.

CALCULATING PERIMETER. WHAT IS PERIMETER? Perimeter is the total length or distance around a figure. CALCULATING PERIMETER WHAT IS PERIMETER? Perimeter is the total length or distance around a figure. HOW DO WE CALCULATE PERIMETER? The formula one can use to calculate perimeter depends on the type of

More information

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

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

More information

Solutions Section J: Perimeter and Area

Solutions Section J: Perimeter and Area Solutions Section J: Perimeter and Area 1. The 6 by 10 rectangle below has semi-circles attached on each end. 6 10 a) Find the perimeter of (the distance around) the figure above. b) Find the area enclosed

More information

The area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2

The area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2 The area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2 s s rectangle: A = l w parallelogram: A = b h h b triangle:

More information

G6-9 Area of Composite Shapes

G6-9 Area of Composite Shapes G6-9 Area of Composite Shapes 1. a) Calculate the area of each figure. b) Draw a line to show how Shape C can be divided into rectangles A and. i) ii) A C A C Area of A = Area of A = Area of = Area of

More information

POOLS The diagram of the pool from the beginning of the lesson is shown below. Find the area of the pool s floor. 28 ft. 6 ft. 4 ft.

POOLS The diagram of the pool from the beginning of the lesson is shown below. Find the area of the pool s floor. 28 ft. 6 ft. 4 ft. Multi-Part Lesson 9-3 PART Main Idea Find areas of composite figures. glencoe.com Composite Figures A C B D Area of Composite Figures 8 ft POOLS The dimensions of a pool at recreation center are shown..

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

The formula for the area of a parallelogram is: A = bh, where b is the length of the base and h is the length of the height.

The formula for the area of a parallelogram is: A = bh, where b is the length of the base and h is the length of the height. The formula for the area of a parallelogram is: A = h, where is the length of the ase and h is the length of the height. The formula for the area of a parallelogram is: A = h, where is the length of the

More information

Area and Perimeter. Name: Class: Date: Short Answer

Area and Perimeter. Name: Class: Date: Short Answer Name: Class: Date: ID: A Area and Perimeter Short Answer 1. The squares on this grid are 1 centimeter long and 1 centimeter wide. Outline two different figures with an area of 12 square centimeters and

More information

Geometry Notes PERIMETER AND AREA

Geometry Notes PERIMETER AND AREA Perimeter and Area Page 1 of 17 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

Lesson 3: Area. Selected Content Standards. Translating Content Standards into Instruction

Lesson 3: Area. Selected Content Standards. Translating Content Standards into Instruction Lesson 3: Area Selected Content Standards Benchmark Assessed: M.3 Estimating, computing, and applying physical measurement using suitable units (e.g., calculate perimeter and area of plane figures, surface

More information

Signs, Signs, Every Place There Are Signs! Area of Regular Polygons p. 171 Boundary Lines Area of Parallelograms and Triangles p.

Signs, Signs, Every Place There Are Signs! Area of Regular Polygons p. 171 Boundary Lines Area of Parallelograms and Triangles p. C H A P T E R Perimeter and Area Regatta is another word for boat race. In sailing regattas, sailboats compete on courses defined by marks or buoys. These courses often start and end at the same mark,

More information

12-4 Volumes of Prisms and Cylinders. Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h

12-4 Volumes of Prisms and Cylinders. Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h The volume is 108 cm 3. The volume V of a prism is V = Bh, where B is the area of a base and h the

More information

A. Areas of Parallelograms 1. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh.

A. Areas of Parallelograms 1. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh. Geometry - Areas of Parallelograms A. Areas of Parallelograms. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh. A B Ex: See how VDFA V CGB so rectangle

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

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

12-4 Volumes of Prisms and Cylinders. Find the volume of each prism.

12-4 Volumes of Prisms and Cylinders. Find the volume of each prism. Find the volume of each prism. 3. the oblique rectangular prism shown at the right 1. The volume V of a prism is V = Bh, where B is the area of a base and h is the height of the prism. If two solids have

More information

b = base h = height Area is the number of square units that make up the inside of the shape is a square with a side length of 1 of any unit

b = base h = height Area is the number of square units that make up the inside of the shape is a square with a side length of 1 of any unit Area is the number of square units that make up the inside of the shape of 1 of any unit is a square with a side length Jan 29-7:58 AM b = base h = height Jan 29-8:31 AM 1 Example 6 in Jan 29-8:33 AM A

More information

Perimeter and Area. An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this.

Perimeter and Area. An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this. UNIT 10 Perimeter and Area An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this. 3 UNIT 10 PERIMETER AND AREA You can find geometric shapes in

More information

Math 6: Unit 7: Geometry Notes 2-Dimensional Figures

Math 6: Unit 7: Geometry Notes 2-Dimensional Figures Math 6: Unit 7: Geometry Notes -Dimensional Figures Prep for 6.G.A.1 Classifying Polygons A polygon is defined as a closed geometric figure formed by connecting line segments endpoint to endpoint. Polygons

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

Geometry Chapter 9 Extending Perimeter, Circumference, and Area

Geometry Chapter 9 Extending Perimeter, Circumference, and Area Geometry Chapter 9 Extending Perimeter, Circumference, and Area Lesson 1 Developing Formulas for Triangles and Quadrilaterals Learning Target (LT-1) Solve problems involving the perimeter and area of triangles

More information

Are You Ready? Circumference and Area of Circles

Are You Ready? Circumference and Area of Circles SKILL 39 Are You Read? Circumference and Area of Circles Teaching Skill 39 Objective Find the circumference and area of circles. Remind students that perimeter is the distance around a figure and that

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

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

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

Geometry Chapter 9 Extending Perimeter, Circumference, and Area

Geometry Chapter 9 Extending Perimeter, Circumference, and Area Geometry Chapter 9 Extending Perimeter, Circumference, and Area Lesson 1 Developing Formulas for Triangles and Quadrilaterals Learning Targets LT9-1: Solve problems involving the perimeter and area of

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

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

More information

PART 3 MODULE 8 PROBLEMS INVOLVING AREA

PART 3 MODULE 8 PROBLEMS INVOLVING AREA PART 3 MODULE 8 PROBLEMS INVOLVING AREA We will be examining a variety of real-world problems that can be solved by referring to familiar facts from elementary geometry. These problems will usually require

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

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

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

Integrated Algebra: Geometry

Integrated Algebra: Geometry Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

More information

1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft

1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft 2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite

More information

Lesson 7: Using Formulas

Lesson 7: Using Formulas Lesson 7: Using Formulas Steps for Solving Problems Using a Formula 1. 2. 3. 4. Example 1 Using the formula: Density = mass/volume or D = m/v Find the density of a rock that has a volume of 20 ml with

More information

A = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height

A = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height Formula Key b 1 base height rea b or (b 1 / b for a trapezoid) h b Perimeter diagonal P d (d 1 / d for a kite) d 1 d Perpendicular two lines form a angle. Perimeter P = total of all sides (side + side

More information

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry. Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know

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

11-4 Areas of Regular Polygons and Composite Figures

11-4 Areas of Regular Polygons and Composite Figures 1. In the figure, square ABDC is inscribed in F. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle. Center: point F, radius:, apothem:,

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

MATH STUDENT BOOK. 7th Grade Unit 9

MATH STUDENT BOOK. 7th Grade Unit 9 MATH STUDENT BOOK 7th Grade Unit 9 Unit 9 Measurement and Area Math 709 Measurement and Area Introduction 3 1. Perimeter 5 Perimeter 5 Circumference 11 Composite Figures 16 Self Test 1: Perimeter 24 2.

More information

Formulas for Area Area of Trapezoid

Formulas for Area Area of Trapezoid Area of Triangle Formulas for Area Area of Trapezoid Area of Parallelograms Use the formula sheet and what you know about area to solve the following problems. Find the area. 5 feet 6 feet 4 feet 8.5 feet

More information

Perimeter and area formulas for common geometric figures:

Perimeter and area formulas for common geometric figures: Lesson 10.1 10.: Perimeter and Area of Common Geometric Figures Focused Learning Target: I will be able to Solve problems involving perimeter and area of common geometric figures. Compute areas of rectangles,

More information

Geometry. 2 h (b + b ), where b and b are the bases ). More Ideas. Formative Assessment

Geometry. 2 h (b + b ), where b and b are the bases ). More Ideas. Formative Assessment 4 Objective Area of Trapezoids By the time students reach 7th and 8th grade, they are expected to bring to their study of geometry and measurement an understanding of common figures such as squares, rectangles,

More information

10.1 Areas of Quadrilaterals and triangles

10.1 Areas of Quadrilaterals and triangles 10.1 Areas of Quadrilaterals and triangles BASE AND HEIGHT MUST FORM A RIGHT ANGLE!! Draw the diagram, write the formula and SHOW YOUR WORK! FIND THE AREA OF THE FOLLOWING:. A rectangle with one side of

More information

Grade 4 Mathematics Measurement: Lesson 2

Grade 4 Mathematics Measurement: Lesson 2 Grade 4 Mathematics Measurement: 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

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

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

11-6 Area: Parallelograms, Triangles, and Trapezoids

11-6 Area: Parallelograms, Triangles, and Trapezoids 1. 6. LACROSSE A lacrosse goal with net is shown. The goal is 6 feet wide, 6 feet high, and 7 feet deep. What is the area of the triangular region of the ground inside the net? 30.5 ft 2 2. 21 ft 2 14.08

More information

AREA AND PERIMETER OF COMPLEX PLANE FIGURES

AREA AND PERIMETER OF COMPLEX PLANE FIGURES AREA AND PERIMETER OF OMPLEX PLANE FIGURES AREA AND PERIMETER OF POLYGONAL FIGURES DISSETION PRINIPLE: Every polygon can be dissected (or broken up) into triangles (or rectangles), which have no interior

More information

8-8 Volume and Surface Area of Composite Figures. Find the volume of the composite figure. Round to the nearest tenth if necessary.

8-8 Volume and Surface Area of Composite Figures. Find the volume of the composite figure. Round to the nearest tenth if necessary. Find the volume of the composite figure. Round to the nearest tenth if necessary. The figure is made up of a triangular prism and a rectangular prism. Volume of triangular prism The figure is made up of

More information

Lesson 25: Volume of Right Prisms

Lesson 25: Volume of Right Prisms Lesson 25 Lesson 25: Volume of Right Prisms Classwork Opening Exercise Take your copy of the following figure, and cut it into four pieces along the dotted lines (the vertical line is the altitude, and

More information

Archdiocese of Washington Catholic Schools Academic Standards Mathematics

Archdiocese of Washington Catholic Schools Academic Standards Mathematics 5 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,

More information

Model area formulas for parallelograms, trapezoids, and triangles.

Model area formulas for parallelograms, trapezoids, and triangles. Answers Teacher Copy Lesson 23-3 Area of Triangles, Trapezoids, and Polygons Learning Targets p. 297 Model area formulas for parallelograms, trapezoids, and triangles. Write equations that represent problems

More information

LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.

LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable. Name LEVEL G, SKILL 1 Class Be sure to show all work.. Leave answers in terms of ϖ where applicable. 1. What is the area of a triangle with a base of 4 cm and a height of 6 cm? 2. What is the sum of the

More information

Name: School Team: X = 5 X = 25 X = 40 X = 0.09 X = 15

Name: School Team: X = 5 X = 25 X = 40 X = 0.09 X = 15 7th/8th grade Math Meet Name: School Team: Event : Problem Solving (no calculators) Part : Computation ( pts. each) ) / + /x + /0 = X = 5 ) 0% of 5 = x % of X = 5 ) 00 - x = ()()(4) + 6 X = 40 4) 0.6 x

More information

I Perimeter, Area, Learning Goals 304

I Perimeter, Area, Learning Goals 304 U N I T Perimeter, Area, Greeting cards come in a variety of shapes and sizes. You can buy a greeting card for just about any occasion! Learning Goals measure and calculate perimeter estimate, measure,

More information

Math Tech 1 Unit 11. Perimeter, Circumference and Area. Name Pd

Math Tech 1 Unit 11. Perimeter, Circumference and Area. Name Pd Math Tech 1 Unit 11 Perimeter, Circumference and Area Name Pd 11-1 Perimeter Perimeter - Units - Ex. 1: Find the perimeter of a rectangle with length 7 m and width 5 m. Ex. 2: Find the perimeter of the

More information

How do changes in dimensions of similar geometric figures affect the perimeters and the areas of the figures? ACTIVITY: Creating Similar Figures

How do changes in dimensions of similar geometric figures affect the perimeters and the areas of the figures? ACTIVITY: Creating Similar Figures .6 Perimeters and Areas of Similar Figures How do changes in dimensions of similar geometric figures affect the perimeters and the areas of the figures? ACTIVITY: Creating Similar Figures Work with a partner.

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

AREA. AREA is the amount of surface inside a flat shape. (flat means 2 dimensional)

AREA. AREA is the amount of surface inside a flat shape. (flat means 2 dimensional) AREA AREA is the amount of surface inside a flat shape. (flat means 2 dimensional) Area is always measured in units 2 The most basic questions that you will see will involve calculating the area of a square

More information

Basic Garden Math. This document is organized into the following sections:

Basic Garden Math. This document is organized into the following sections: Basic Garden Math Gardening is an activity which occasionally requires the use of math, such as when you are computing how much fertilizer to use or how much compost to buy. Luckily, the math involved

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

Composite Figures. Learning Objectives. Pre-Activity

Composite Figures. Learning Objectives. Pre-Activity Section 3.6 Pre-ctivity Preparation Composite Figures Leisure activities often include the use of different combinations of basic shapes. Below are some examples of how we might use basic shapes in complex

More information

The Area is the width times the height: Area = w h

The Area is the width times the height: Area = w h Geometry Handout Rectangle and Square Area of a Rectangle and Square (square has all sides equal) The Area is the width times the height: Area = w h Example: A rectangle is 6 m wide and 3 m high; what

More information

You can use the postulates below to prove several theorems.

You can use the postulates below to prove several theorems. Using Area Formulas You can use the postulates below to prove several theorems. AREA POSTULATES Postulate Area of a Square Postulate The area of a square is the square of the length of its side, or s.

More information

Solids: Surface Area and Volume. 1. Use four cubes of the same size to build shapes such as the ones shown

Solids: Surface Area and Volume. 1. Use four cubes of the same size to build shapes such as the ones shown Solids: Surface Area and Volume 1. Use four cubes of the same size to build shapes such as the ones shown below (others are possible sketch them after you have built them). In each case, nd the surface

More information

*1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle.

*1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle. Students: 1. Students deepen their understanding of measurement of plane and solid shapes and use this understanding to solve problems. *1. Understand the concept of a constant number like pi. Know the

More information

Perimeter, Circumference, Area and Ratio Long-Term Memory Review

Perimeter, Circumference, Area and Ratio Long-Term Memory Review Review 1 1. Which procedure is used to find the perimeter of any polygon? A) Add all the lengths B) Multiply length times width ( l w ) C) Add only one length and one width D) Multiply all of the lengths

More information

MAIN IDEA The rectangle at the right has an area of 20 square units. The distance around the rectangle is 5 + 4 + 5 + 4, or 18 units.

MAIN IDEA The rectangle at the right has an area of 20 square units. The distance around the rectangle is 5 + 4 + 5 + 4, or 18 units. 1-9 Algebra: Area Formulas MAIN IDEA The rectangle at the right has an area of 20 square units. The distance around the rectangle is 5 + 4 + 5 + 4, or 1. Find the areas of rectangles and squares. New Vocabulary

More information

Area and Perimeter Teaching Suggestions:

Area and Perimeter Teaching Suggestions: Area and Perimeter Teaching Suggestions: Use math definition posters to discuss: dimension, two-dimensional shapes, length, width, perimeter and area. Brainstorm examples of each, and develop vocabulary

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

Lesson 3.1 Factors and Multiples of Whole Numbers Exercises (pages 140 141)

Lesson 3.1 Factors and Multiples of Whole Numbers Exercises (pages 140 141) Lesson 3.1 Factors and Multiples of Whole Numbers Exercises (pages 140 141) A 3. Multiply each number by 1, 2, 3, 4, 5, and 6. a) 6 1 = 6 6 2 = 12 6 3 = 18 6 4 = 24 6 5 = 30 6 6 = 36 So, the first 6 multiples

More information

Grade 7 Area of triangle

Grade 7 Area of triangle Grade 7 Area of triangle 7.SS.2 Develop and apply a formula for determining the area of triangles parallelograms circles 1. Illustrate and explain how the area of a rectangle can be used to determine the

More information

STUDENT NAME: GRADE 10 MATHEMATICS

STUDENT NAME: GRADE 10 MATHEMATICS STUDENT NAME: GRADE 10 MATHEMATICS Administered December 2009 Name: Class: 10th Grade TAKS Practice Test 2 1. A portion of isosceles trapezoid NPRT is shown on the grid below. 2. Troy borrowed money from

More information

Line AB (no Endpoints) Ray with Endpoint A. Line Segments with Endpoints A and B. Angle is formed by TWO Rays with a common Endpoint.

Line AB (no Endpoints) Ray with Endpoint A. Line Segments with Endpoints A and B. Angle is formed by TWO Rays with a common Endpoint. Section 8 1 Lines and Angles Point is a specific location in space.. Line is a straight path (infinite number of points). Line Segment is part of a line between TWO points. Ray is part of the line that

More information

Lesson 19: Unknown Area Problems on the Coordinate Plane

Lesson 19: Unknown Area Problems on the Coordinate Plane Lesson 19 Lesson 19: Unknown Area Problems on the Coordinate Plane Student Outcomes Students find the areas of triangles and simple polygonal regions in the coordinate plane with vertices at grid points

More information

Area and Volume Equations

Area and Volume Equations Area and Volume Equations MODULE 16? ESSENTIAL QUESTION How can you use area and volume equations to solve real-world problems? LESSON 16.1 Area of Quadrilaterals 6.8.B, 6.8.D LESSON 16. Area of Triangles

More information

Grade 11 Essential Mathematics Unit 6: Measurement and Geometry

Grade 11 Essential Mathematics Unit 6: Measurement and Geometry Grade 11 Essential Mathematics Unit 6: INTRODUCTION When people first began to take measurements, they would use parts of the hands and arms. For example, a digit was the width of a thumb. This kind of

More information

Perimeter, Circumference, and Area

Perimeter, Circumference, and Area -9 Perimeter, Circumference, and Area -9. Plan What You ll Learn To find perimeters of rectangles and squares, and circumferences of circles To find areas of rectangles, squares, and circles... And Why

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

Geometric Concepts. Academic Vocabulary composite

Geometric Concepts. Academic Vocabulary composite Geometric Concepts 5 Unit Overview In this unit you will extend your study of polygons as you investigate properties of triangles and quadrilaterals. You will study area, surface area, and volume of two-

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

Geometry: A Better Understanding of Area

Geometry: A Better Understanding of Area Geometry: A Better Understanding of Area 6G1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other

More information

Review for Final - Geometry B

Review for Final - Geometry B Review for Final - Geometry B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A model is made of a car. The car is 4 meters long and the model is 7 centimeters

More information

6.3. Surface Area of Solids The Gift Box. My Notes ACTIVITY

6.3. Surface Area of Solids The Gift Box. My Notes ACTIVITY Surface Area of Solids SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge J.T. is the creative director for a paper products company. The company is introducing a new line of gift boxes, called

More information

Pythagorean Theorem, Distance and Midpoints Chapter Questions. 3. What types of lines do we need to use the distance and midpoint formulas for?

Pythagorean Theorem, Distance and Midpoints Chapter Questions. 3. What types of lines do we need to use the distance and midpoint formulas for? Pythagorean Theorem, Distance and Midpoints Chapter Questions 1. How is the formula for the Pythagorean Theorem derived? 2. What type of triangle uses the Pythagorean Theorem? 3. What types of lines do

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

Geometry: Chapter Questions. 1. How is the formula for area of a parallelogram related to area of a rectangle?

Geometry: Chapter Questions. 1. How is the formula for area of a parallelogram related to area of a rectangle? Geometry: Chapter Questions. How is the formula for area of a parallelogram related to area of a rectangle?. How is the formula for area of a triangle related to area of a rectangle?. How do you find the

More information

A.G.1: Compositions of Poygons and Circles 2: Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle

A.G.1: Compositions of Poygons and Circles 2: Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle A.G.1: Compositions of Poygons and Circles 2: Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle 1 In the accompanying figure, ACDH and BCEF are rectangles,

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