Area of Composite Figures - Norwell High School

Name

Class

Date

Area of Composite Figures

Going Deeper

Essential question: How can you find the area of a polygon by breaking it into simpler shapes?

CC.6.G.1

1 E X P L O R E Area Using Tangrams

The area of the small square is 1 square unit. Find the area of each of the other tangram pieces.

8-5

video tutor

1

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A Place one large triangle on top of the other large triangle. What is true about these two triangles? What does this mean about the areas of these two triangles?

B What is true about the areas of the two small triangles?

C Place the two small triangles on top of the square. Remember that the area of

the square is 1. What is the area of each small triangle? this area on the diagram.

Write

D Arrange the square and one of the small triangles as shown.

What is the combined area?

Now place the parallelogram and the other small triangle on top of the combined square and triangle. What is true about the combined area of the parallelogram and one small triangle?

The two small triangles have

area. Therefore, the area of

the parallelogram is the same as the area of the

.

Write the area of the parallelogram on the diagram.

Chapter 8

365

Lesson 5

TRY THIS!

1. Complete the rest of the diagram by filling in the remaining areas. Explain how you found your answers.

CC.6.G.1

2 E X A M P L E Finding the Area of a Polygon

Find the area of each polygon.

A

5

3 6

8

Step 1Draw a horizontal line segment on the diagram that divides the polygon into two rectangles, one on top of the other.

What is the length of this segment? the diagram.

Label this length on

Step 2Find the area of the smaller (top) rectangle.

A = bh =

?

=

square units

Step 3 Find the area of the larger (bottom) rectangle.

The base of the larger rectangle is

.

The height is 6 -

=

.

A = bh =

?

=

square units

Step 4 Add the areas from Steps 2 and 3 to find the total area.

A =

+

=

square units

REFLECT

2a. Redraw the original polygon. Divide the polygon into two rectangles in a different way and use these two rectangles to find the area.

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2b. Does the way you divide the original polygon affect the final answer?

Chapter 8

366

Lesson 5

B

2

6 3

6

Step 1On the diagram, form a square with a "missing piece": Extend the top side of the polygon to the right and extend the right side of the polygon up.

What is the side length of this square?

The area of the square is

?

=

square units.

Step 2 Find the area of the rectangular "missing piece".

b = 6 - 2 =

h = 6 -

=

A = bh =

?

=

square units

Step 3 Subtract the area in Step 2 from the area in Step 1.

A =

-

=

square units

C 13

8 7

16

Step 1Draw a horizontal line segment on the diagram that divides the polygon into a rectangle and a triangle.

Step 2 Find the area of the rectangle.

A = bh =

?

=

square units

Step 3 Find the area of the triangle.

b = 16 -

=

h = 13 -

=

A = _12_bh = _12_?

?

=

square units

Step 4 Add the areas from Steps 2 and 3 to find the total area.

A =

+

=

square units

TRY THIS!

Find the area of each polygon.

2c.

18

9 18

A =

36

square units

4

2d.

3

6

8

3

A =

square units

Chapter 8

367

Lesson 5

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pra c t i c e

Find the area of each polygon.

1.

4

2.

10 14

14 8

18

20

A =

square units

A =

square units

3.

1

3

1

4 1

1

4.

9

5

12

A =

square units

A =

5. In Hal's backyard, there is a patio, a walkway, and a garden.

6 ft

2.5

2.5

square units

Patio 5 ft

Lawn

Walkway

Lawn

Garden

3 ft

8 ft

9 ft

a.Show how to find the total area of the patio, walkway, and garden by adding areas of rectangles.

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b.Show how to find the total area of the patio, walkway, and garden by subtracting areas of rectangles.

Chapter 8

368

Lesson 5

Name

Class

Date

8-5

Name ________________________________________ Date __________________ Class__________________

ALEdSSOdN iMteioasnuarelmPenrtaacndtiGceeometry 5 Practice B: Area of Composite Figures

Find the area of each polygon.

1.

2.

________________________________________

3.

________________________________________

4.

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________________________________________

5.

________________________________________

6.

________________________________________

________________________________________

7. Three paintings are shaped like an 8-foot square, a 7-foot by 4-foot rectangle, and a triangle with a 6-foot base and a height of 7 feet. If those paintings are hung together on the outside of a building, how much of the building's wall will they cover altogether?

_________________________________________________________________________________________

8. Two diagonals divide a square carpet into 4 congruent triangles. The base of each triangle is 5 feet and the height is 2.5 feet. What is the area of the entire carpet?

_________________________________________________________________________________________

Chapter 8

369 53

Practice and Problem Solving Holt McDougal Mathematics

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