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1. True or false: If the height of a rectangle equals the base of a parallelogram and the base of the rectangle equals the height of the parallelogram, then the rectangle and the parallelogram have the same area.

2. Find the area of a rectangle with a length of 53 in. and a width of 47 in.

True

2,491 in2

Learn to find the area of triangles and trapezoids.

You can divide any parallelogram into two congruent triangles. So the area of each triangle is half the area of the parallelogram.

Additional Example 1A: Finding the Area of a Triangle triangles. So the area of each triangle is half the area of the parallelogram.

Find the area of the triangle.

1

2

bh

A =

Write the formula.

1

2

Substitute 20for b and 12for h.

(20· 12)

A =

1

2

Multiply.

(240)

A =

A = 120

The area is 120 ft2.

Reading Math triangles. So the area of each triangle is half the area of the parallelogram.

An altitude of a triangle is a perpendicular segment from one vertex to the line containing the opposite side. The length of the altitude is the height.

Additional Example 1B: Finding the Area of a Triangle triangles. So the area of each triangle is half the area of the parallelogram.

Find the area of the triangle.

1

2

bh

A =

Write the formula.

1

2

Substitute 30for b and 24for h.

(30· 24)

A =

1

2

Multiply.

(720)

A =

A = 360

The area is 360 in2.

Check It Out: Example 1A triangles. So the area of each triangle is half the area of the parallelogram.

Find the area of the triangle.

1

2

bh

A =

Write the formula.

1

2

Substitute 5for b and 8for h.

(5· 8)

A =

8 in.

1

2

5 in.

Multiply.

(40)

A =

A = 20

The area is 20 in2.

1 triangles. So the area of each triangle is half the area of the parallelogram.

2

Substitute 4 for b and 24for h.

1

(4 • 24)

A =

1

2

2

1

2

Check It Out: Example 1B

Find the area of the triangle.

1

2

bh

A =

Write the formula.

24 ft

1

2

Multiply.

(108)

A =

A = 54

4 ft

The area is 54 in2.

Additional Example 2: triangles. So the area of each triangle is half the area of the parallelogram.Application

The diagram shows the section of a forest being studied. What is the area of the section?

1

2

bh

A =

Write the formula.

1

2

Substitute 43.9for b. Substitute 16for h.

(43.9 •16)

A =

1

2

Multiply.

(702.4)

A =

A = 351.2

The area is 351.2 km2.

24.5 m triangles. So the area of each triangle is half the area of the parallelogram.

48 m

Check It Out: Example 2

The diagram shows the section of a park being studied. What is the area of the section?

1

2

bh

A =

Write the formula.

1

2

Substitute 48for b. Substitute 24.5for h.

(48· 24.5)

A =

1

2

Multiply.

(1176)

A =

A = 588

The area is 588 m2.

1 triangles. So the area of each triangle is half the area of the parallelogram.

2

Substitute 4 for h, 14 for b1, and 12 for b2.

· 4(14 + 12 )

A =

1

2

1

2

1

2

· 4(26 )

1

A =

2

Additional Example 3: Finding the Area of a Trapezoid

Find the area of the trapezoid.

1

2

h(b1 + b2)

Use the formula.

A =

A = 53

Multiply.

The area is 53 yd2.

Check It Out: Example 3 triangles. So the area of each triangle is half the area of the parallelogram.

12 cm

Find the area of the trapezoid.

7 cm

16 cm

1

2

h(b1 + b2)

Use the formula.

A =

1

2

Substitute 7 for h, 16 for b1, and 12 for b2.

· 7(16 + 12)

A =

1

2

· 7(28)

A =

A = 98

Multiply.

The area is 98 cm2.

Lesson Quizzes triangles. So the area of each triangle is half the area of the parallelogram.

Standard Lesson Quiz

Lesson Quiz for Student Response Systems

3 triangles. So the area of each triangle is half the area of the parallelogram. 4

113 in2

Lesson Quiz

Find the area of each triangle.

1.

3.

2.

39.9 cm2

84 mi2

Find the area of each trapezoid.

4.

22.5 m2

Lesson Quiz for Student Response Systems triangles. So the area of each triangle is half the area of the parallelogram.

1. Find the area of the triangle.

A. 48.3 cm2B. 48.8 cm2

C. 52.3 cm2D. 58.6 cm2

Lesson Quiz for Student Response Systems triangles. So the area of each triangle is half the area of the parallelogram.

2. Find the area of the triangle.

A. 124 m2B. 134 m2

C. 132 m2D. 144 m2

Lesson Quiz for Student Response Systems triangles. So the area of each triangle is half the area of the parallelogram.

3. Find the area of the trapezoid.

A. 37.2 m2B. 35.8 m2

C. 33.4 m2D. 32.6 m2

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