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Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Find the area of each figure. Round to the nearest tenth, if necessary. 1. a trapezoid with bases 10 cm and 12 cm and height 5 m 2. a parallelogram with base 9 in. and height 8 in. 3. a semicircle with radius 5 m

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Presentation Transcript

Preview

Warm Up

California Standards

Lesson Presentation

Warm Up

Find the area of each figure. Round to the nearest tenth, if necessary.

1.a trapezoid with bases 10 cm and 12 cm and height 5 m

2. a parallelogram with base 9 in. and height 8 in.

3. a semicircle with radius 5 m

4. a semicircle with diameter 8 cm

55 cm2

72 in2

39.3 m2

25.1 cm2

California

Standards

MG2.2 Estimate andcompute the area of more complex or irregular two-andthree-dimensional figures by breaking the figures down into more basic geometric objects.

One method of estimating the area of an irregular figure is to count the number of squares the figure covers.

The area of the figure is 12 square units.

Additional Example 1: Finding Area by Counting

Find the area of each figure.

A.

Count the full squares: 10

Count the half-full squares: 4

Add the number of full squares plus half the number of half-full squares:

10 + ( • 4) = 10 + 2 =12

1 2

For shapes such as the one in Example 1B you can only estimate the area.

The area of the figure is approximately 13 square units.

Additional Example 1: Finding Area by Counting

Find the area of each figure.

B.

Count the full and almost-full squares: 11

Count the half-full squares: 4

Add the number of full squares plus half the number of half-full squares:

11 + ( • 4) = 11 + 2 =13

1 2

The area of the figure is 15 square units.

Check It Out! Example 1

Find the area of each figure.

A.

Count the full squares: 11

Count the half-full squares: 8

Add the number of full squares plus half the number of half-full squares:

11 + ( • 8) = 11 + 4 = 15

1 2

The area of the figure is about 14 square units.

Check It Out! Example 1

Find the area of each figure.

B.

Count the full and almost-full squares: 11

Count the half-full squares: 6

Add the number of full squares plus half the number of half-full squares:

11 + ( • 6) = 11 + 3 =14

1 2

Use a composite figure to estimate the shaded area.

Draw a composite figure that approximates the irregular shape. Divide the composite figure into simple shapes.

1

1

__

__

2

2

1 2

1 2

area of the trapezoid:

area of the triangle:

A = bh

= (4•2) = 4

The shaded area is approximately 7 square units.

A = h(b1+ b2)

= 1(4 +2)= 3

Use a composite figure to estimate the shaded area.

Use a composite figure to estimate the shaded area.

Draw a composite figure that approximates the irregular shape. Divide the composite figure into simple shapes.

1

1

__

__

2

2

A =bh

= 1 •4 = 4

area of the rectangle:

area of the semicircle:

A = pr2

•3.14(22)

 6.28

The shaded area is approximately 10.3 square units.

Use a composite figure to estimate the shaded area.

Check It Out! Example 2A

Use a composite figure to estimate the shaded area.

Draw a composite figure that approximates the irregular shape. Divide the composite figure into simple shapes.

1

1

__

__

2

2

A =bh

= 3 •2 = 6

area of the rectangle:

area of the triangle:

A = bh

= (3•2) = 3

The shaded area is approximately 9 square units.

Check It Out! Example 2A Continued

Use a composite figure to estimate the shaded area.

Check It Out! Example 2B

Use a composite figure to estimate the shaded area.

Draw a composite figure that approximates the irregular shape. Divide the composite figure into simple shapes.

1

1

__

__

2

2

A =s2

= 2 •2= 4

area of the square:

area of the semicircle:

A = pr2

•3.14(12)

 1.57

The shaded area is approximately 5.5 square units.

Check It Out! Example 2B Continued

Use a composite figure to estimate the shaded area.

8 square units

approximately 12 square units

Lesson Quiz: Part l

Find the area of each figure.

1.

2.

approximately 4 square units

approximately 6 square units

Lesson Quiz: Part ll

Use a composite figure to estimate the shaded area.

3.

4.

1 2