10-3 Area of Composite Figures

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

10-3 Area of Composite Figures

Warm Up

1. What is the area of a rectangle with length 10 cm and width 4 cm?

2. What is the area of a parallelogram with base 18 ft and height 12 ft?

3. What is the area of a triangle with base 16 cm and height 8 cm?

40 cm2

216 ft2

64 cm2

10-3 Area of Composite Figures

Problem of the Day

Four squares are placed in a row. The square on the far left is 12 inches on a side. The perimeter of each of the other squares is half of the one to its left. What is the perimeter of the combined figure?

69 in.

10-3 Area of Composite Figures

Learn to break a polygon into simpler parts to find its area.

10-3 Area of Composite FiguresAdditional Example 1A: Finding Areas of Composite

Figures

Find the area of the polygon.

Think: Break the polygon apart into rectangles.

Find the area of each rectangle.

1.7 cm

4.9 cm 1.3 cm

2.1 cm

10-3 Area of Composite FiguresAdditional Example 1A Continued

A = lw A = lw

A = 4.9 • 1.7 A = 2.1 • 1.3Write the formula for the area of a rectangle.A = 8.33 A = 2.73

8.33 + 2.73 = 11.06 Add to find the total area.

The area of the polygon is 11.06 cm2.

1.7 cm

4.9 cm

1.3 cm

2.1 cm

10-3 Area of Composite Figures

Think: Break the figure apart into a rectangle and a triangle.

Find the area of each polygon.

Additional Example 1B: Finding Areas of Composite Figures

Find the area of the polygon.

10-3 Area of Composite FiguresAdditional Example 1B Continued

A = lw

A = 28 • 24

A = 672 A = 168

672 + 168 = 840 Add to find the total area of the polygon.

The area of the polygon is 840 ft2.

A = bh12__

A = • 28 • 1212__

10-3 Area of Composite FiguresCheck It Out: Example 1A

Find the area of the polygon.

Think: Break the polygon apart into rectangles.

Find the area of each rectangle.

1.9 cm

1.5 cm

2 cm

3.4 cm

5.5 cm

1.9 cm

5.5 cm 1.5 cm

2 cm

10-3 Area of Composite Figures

A = lw A = lw

A = 5.5 • 1.9 A = 2 • 1.5Write the formula for the area of a rectangle.A = 10.45 A = 3

10.45 + 3 = 13.45 Add to find the total area.

The area of the polygon is 13.45 cm2.

Check It Out: Example 1A Continued

1.9 cm

5.5 cm 1.5 cm

2 cm

10-3 Area of Composite FiguresCheck It Out: Example 1B

Find the area of the polygon.

Think: Break the figure apart into a rectangle and a triangle.

Find the area of each polygon.

36 ft

22 ft

20 ft

20 ft

22 ft

22 ft

16 ft

10-3 Area of Composite Figures

A = lw

A = 22 • 20

A = 440 A = 176

440 + 176 = 616 Add to find the total area of the polygon.

The area of the polygon is 616 ft2.

A = bh12__

A = • 22 • 1612__

Check It Out: Example 1B Continued

20 ft22 ft

22 ft

16 ft

10-3 Area of Composite FiguresAdditional Example 2: Art Application

Patrick made a design. Use the coordinate grid to find its area.

Think: Divide the design into rectangles. Find the area of each rectangle.Rectangle 1

l = 5, w = 5; A = 5 • 5 = 25

Rectangle 2l = 10, w = 5; A = 10 • 5 = 50

Rectangle 3l = 15, w = 5; A = 15 • 5 = 75

Rectangle 4l = 20, w = 5; A = 20 • 5 = 100

0

10

15

20

5 10

5

15 20 25

25

10-3 Area of Composite FiguresAdditional Example 2 Continued

25 + 50 + 75 + 100 = 250 square units.

Add the areas of the four rectangles to find the total area of the design.

The area of the design is 250 square units.

10-3 Area of Composite Figures

You can also count the squares and multiply by the area of one square. 1 square = 25 square units. 10 • 25 = 250 square units.

Helpful Hint

10-3 Area of Composite Figures

Check It Out: Example 2

Lawanda made a design. Use the coordinate grid to find its area.

Think: Divide the design into rectangles. Find the area of each rectangle.

Rectangle 1

l = 5, w = 10; A = 5 • 10 = 50

Rectangle 2l = 5, w = 15; A = 5 • 15 = 75

Rectangle 3l = 5, w = 10; A = 5 • 10 = 50

0

10

15

20

5 10

5

15 20 25

3

2

1

25

10-3 Area of Composite Figures

Check It Out: Example 2 Continued

50 + 75 + 50 = 175 square units.

Add the areas of the three rectangles to find the total area of the design.

The area of the design is 175 square units.

10-3 Area of Composite Figures

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

10-3 Area of Composite Figures

Lesson Quiz

1. Find the area of the figure shown.

220 units2

2. Phillip designed a countertop. Use the coordinate grid to find its area.

30 units2

10-3 Area of Composite Figures

1. Find the area of the figure.

A. 27 units2 B. 54 units2

C. 93 units2 D. 98 units2

Lesson Quiz for Student Response Systems

10-3 Area of Composite Figures

2. Paul arranged tiles to form a model. Use the coordinate grid to identify its area.

A. 25 square unitsB. 18 square units C. 21 square units D. 16 square units

Lesson Quiz for Student Response Systems