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Warm Up

California Standards

Lesson Presentation

Warm Up Find the area of the following

figures. 1. a triangle with a base of 12.4 m and

a height of 5 m 2. a parallelogram with a base

of 36 in. and a height of 15 in. 3. a square

with side lengths of 2.5 yd

31 m2

540 in2

6.25 yd2

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Vocabulary

composite figure

A composite figure is made up of simple geometric

shapes, such as triangles and rectangles. You can

find the area of composite and other irregular

figures by separating them into non-overlapping

familiar figures. The sum of the areas of these

figures is the area of the entire figure. You can

also estimate the area of irregular figures by

using graph paper.

Teacher Example 1 Estimating the Area of an

Irregular Figure Estimate the area of the figure.

Each square represents one square yard.

Count the number of filled or almost-filled

squares 47 squares.

Count the number of squares that are about

half-full 9 squares.

Add the number of filled squares plus ½ the

number of half-filled squares 47 ( 9)

47 4.5 51.5

1 2

Student Practice 1 Estimate the area of the

figure. Each square represents 1 yd2.

Count the number of filled or almost-filled

squares 11 red squares.

Count the number of squares that are about

half-full 8 green squares.

Add the number of filled squares plus ½ the

number of half-filled squares 11 ( 8)

11 4 15.

1 2

Teacher Example 2 Finding the Area of a

Composite Figure Find the area of the composite

figure. Use 3.14 as an estimate for p.

16 m

9 m

16 m

Use the formula for the area of a parallelogram.

Substitute 16 for b.

Substitute 9 for h.

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Teacher Example 2 Continued Find the area of the

composite figure. Use 3.14 as an estimate for p.

The area of a semicircle is the area of a

circle.

12

Substitute 3.14 for p and 8 for r.

Multiply.

Teacher Example 2 Continued Find the area of the

composite figure. Use 3.14 as an estimate for p.

Student Practice 2 Find the area of the

composite figure.

9 yd

2 yd

8 yd

Use the formula for the area of a rectangle.

Substitute 8 for l.

Substitute 9 for w.

Student Practice 2 Continued Find the area of

the composite figure.

9 yd

Substitute 2 for b and 9 for h.

2 yd

8 yd

Multiply.

Student Practice 2 Continued Find the area of

the composite figure. Use 3.14 as an estimate for

p.

Teacher Example 3 Problem Solving

Application The Wrights want to tile their entry

with one-square-foot tiles. How much tile will

they need?

Teacher Example 3 Continued

Rewrite the question as a statement. Find the

amount of tile needed to cover the entry

floor. List the important information The

floor of the entry is a composite figure. The

amount of tile needed is equal to the area of the

floor.

Teacher Example 3 Continued

Find the area of the floor by separating the

figure into familiar figures a rectangle and a

trapezoid. Then add the areas of the rectangle

and trapezoid to find the total area.

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Teacher Example 3 Continued

Find the area of each smaller figure.

Teacher Example 3 Continued

Look Back

The area of the entry must be greater than the

area of the rectangle (40 ft2), so the answer is

reasonable.

Student Practice 3 The Franklins want to

wallpaper the wall of their daughters loft. How

much wallpaper will they need?

Student Practice 3 Continued

Rewrite the question as a statement. Find the

amount of wallpaper needed to cover the loft

wall. List the important information The

wall of the loft is a composite figure. The

amount of wallpaper needed is equal to the area

of the wall.

Student Practice 3 Continued

Find the area of the wall by separating the

figure into familiar figures a rectangle and a

triangle. Then add the areas of the rectangle and

triangle to find the total area.

Student Practice 3 Continued

Find the area of each smaller figure.

Student Practice 3 Continued

Look Back

The area of the wall must be greater than the

area of the rectangle (108 ft2), so the answer is

reasonable.

Lesson Quiz

Find the perimeter and area of each figure. 1.

2.

6 cm

8 cm

10 ft

8.1 ft

7 ft

14 ft