Composite Area

Written by: James Wiens

Newton, Kansas

8cm

5

Instructor Notes

• Subject Area(s): Math• Grade level: 7th grade• Lesson Length: 50 minute class period• Synopsis: Solve for area of composite figures• Objective/goals: Students will find the area of

composite figures by breaking them into common shapes with formulas such as triangles, quadrilaterals and circles.

• Standard: • c. Kansas standard 7.3.2.A1c▲ ■ finding perimeter and area of two-

dimensional composite figures of squares, rectangles, and triangles (2.4.A1h), e.g., the front of a barn is rectangular in shape with a height of 10 feet and a width of 48 feet. Above the rectangle is a triangle that is 7 feet high with sides 25 feet long. What is the area of the front of the barn?

• Pre-requisite skills: Vocabulary – Area, base, height, triangle, paralellogram, trapezoid, pi, radius, circle.

• TurningPoint functions: standard question slides

• Materials: All instructional points and practice problems are provided within the power point slides. Practice questions are designed to be used with the TurningPoint clickers.

Instructor Notes

Lesson Outline

I. Warm-up: find area of basic shapes

II. Definitions / Key Concepts

III. Setting the Stage: Video lesson

IV. Guided practice: Turning Point Questions

V. Independent practice: Paper & pencil

VI. Closure: Write about area

Find the area.

19

in2

44

in2

88

in2

33%33%33%

8in

11in

a) 19 in2

b) 44 in2

c) 88 in2

Countdown

10

Answer

• Area parallelogram = base x height

• A = bh• A = 8 (11)• A = 88 in.2

Find the area.

30 100

1000

100%

0%0%

a) 30 in2

b) 60 in2

c) 120 in2

6in

10in

Countdown

10

Answer

• Area triangle = ½ (base x height)

• A = ½ bh• A = ½ (6)(10)• A = ½ (60)• A = 30 in.2

Find the area. (Use 3.14 for π)

30 100

1000

100%

0%0%

a) 62.8 in2

b) 314 in2

c) 31.4 in2

10in

Countdown

10

Answer

• Area circle = π r2

• A = π r2 • A = π (10)2 • A = π (100)• A = 314 in.2

Definition

• Area of complex figures• To find the area of a complex

figure, break the shape into two or more simple figures. Find the area for the simple figures then combine those amounts to find the total of the complex figure.

Setting the Stage

• How much area does the blue figure cover?

4

3

9 4

Answer

• A = bh • A= 4 (9)• A = 36 in.2

• A = ½ bh• A = ½ (4)(3)• A = ½ (12)• A = 6 in.2

Final Answer:

36 + 6 = 42 in.2

Video Clip Lesson from Teacher Tube

• Click on the link at the right to access a lesson about area of composite figures from Holt Mathematics.

Click here to see the lesson

What is the area of this figure?

A. 36 cm2

B. 54 cm2

C. 45 cm2

D. 18 cm2

912

6

3

3

3 cm

Countdown

10

What is the area of this figure rounded to the nearest cm2?

(Use 3.14 for π)

A. 40 cm2

B. 90 cm2

C. 126 cm2

D. 241 cm2

8cm

5

Countdown

10

What is the area of this figure?

A. 114 cm2

B. 108 cm2

C. 87 cm2

D. 72 cm2

12

268

2

5

Countdown

10

Independent Practice - Find the area of each figure rounded to the nearest foot (All units in feet ).

B.

A.

D.

C.

6 10

7

10

55

30

50

15

6

30

14

4

4

12

50

Answer Key for Independent Practice

A. = 200 ft.2

B. = 210 ft.2

C. = 8500 ft.2

D. = 130 ft.2

Closure / Summary

• Explain how finding the area of a right angle trapezoid is the same as using the sum of the areas of a triangle and a rectangle.

References

• Video clip from slide # 14 found at http://my.hrw.com/math06_07/nsmedia/lesson_videos/msm1/player.html?contentSrc=6072/6072.xml (Holt McDougal math series, Houghton Mifflin Harcourt.)

• Remainder of lesson designed and written by James Wiens, 7th grade math teacher, Newton Kansas.