10-3 Break into Simpler Parts

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Chapter 10 Section 2HOMEWORK Answers

Page 506

#9-16 ALL

Chapter 10 Section 36th Grade Math HOMEWORK

Page 510

#1-6 & #10-14

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

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10-3 Break into Simpler Parts

Problem of the Day

Four squares are stacked in a tower. The bottom square is 12 inches on a side. The perimeter of each of the other squares is half of the one below it. What is the perimeter of the combined figure?

69 in.

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10-3 Break into Simpler Parts

Today’s Learning Goal Assignment

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

Course 1

10-3 Break into Simpler Parts

Additional Example 1A: Finding Areas of Composite Figures

Find the area of the polygon.

A.

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

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10-3 Break into Simpler Parts

Additional 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

Course 1

10-3 Break into Simpler Parts

Additional Example 1B Continued

Find the area of the polygon.

B.

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

Find the area of each polygon.Course 1

10-3 Break into Simpler Parts

Additional 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__

Course 1

10-3 Break into Simpler Parts

Try This: Example 1A

Find the area of the polygon.

A.

Think: Break the polygon apart into rectangles.

Find the area of each rectangle.

1.9 cm

5.5 cm 1.5 cm 2 cm

1.9 cm

1.5 cm

2 cm

3.4 cm

5.5 cm

Course 1

10-3 Break into Simpler Parts

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.

Try This: Example 1A Continued

1.9 cm

5.5 cm 1.5 cm 2 cm

Course 1

10-3 Break into Simpler Parts

Try This: Example 1B

Find the area of the polygon.

B.

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

Course 1

10-3 Break into Simpler Parts

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__

Try This: Example 1B Continued

20 ft22 ft

22 ft

16 ft

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10-3 Break into Simpler Parts

Additional Example 2: Art Application

Patrick made a design. All the sides are 5 inches long, except for two longer sides that are each 20 inches. All the angles are right angles. What is the area of the quilt design?

Think: Divide the design into 3 rectangles. Find the area of one rectangle that has a length of 20 in and a width of 5 in.Write the formula.A = lw

A = 20 • 5 = 100

3 • 100 = 300 Multiply to find the area of the 3 rectangles.

The area of the design is 300 in2.

20 in.

20 in.

5 in.

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10-3 Break into Simpler Parts

You can also use the formula A = s2 , where s is the length of a side, to find the area of a square.

Helpful Hint

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10-3 Break into Simpler Parts

Try This: Example 2

Yvonne made quilt design. All the sides are 4 inches long, except for the two longer sides that are each 16 inches. All the angles are right angles. What is the area of the quilt design?

Think: Divide the quilt design into 10 squares. Find the area of one square that has a side length of 4 in.

Write the formula.A = lw

A = 4 • 4 = 16

10 • 16 = 160Multiply to find the area of the 10 squares.

The area of the quilt design is 160 in2.

4 in.16 in.

16 in.

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10-3 Break into Simpler Parts

Lesson Quiz

Find the area of the figure shown.

Insert Lesson Title Here

220 units2

Course 1

10-3 Break into Simpler Parts