Area of Trapezoids

Given the formula for the area of a parallelogram we are going to use that information to discover the

formula for the area of a trapezoid.

Watch carefully not to miss it!

Notice that the trapezoid is half the area of the parallelogram.

(b1 + b2)

h

Copy the trapezoid, flip it over, and put it next to the original. It makes a parallelogram.

We are going to use the area of a parallelogram to find the area of a trapezoid. It takes two trapezoids to make one parallelogram.

(b1 + b2)

h

Parallelogram

Trapezoid

Notice that the trapezoid is half the area of the parallelogram.How do we find

half the area?

A = (b1 + b2) • h

Hint: Think of area of a triangle.

hbA 2

1

Area of Trapezoid

2 in

6 in

3 in A = (b1 + b2) • h

4 in

2

1

A = (2 + 6) • 32

1

A = (8) • 32

1

A = 4 • 3A = 12 in²

Area of Trapezoid

3 m

8 m

4 m 5 m A = (b1 + b2) • h

2

1

A = (3 + 8) • 42

1

A = (11) • 42

1

A = (44)

A = 22 m²

2

1

4 in

5 in

7 in

6 in

A = 24 in²

5 in

12 in

7 in

A = 59.5 in²

Find the HEIGHT of the Trapezoid

7 ft

15 ft

A = (b1 + b2) • h2

1

88 = (15 + 7) • h2

1

88 = (22) • h2

1

88 = 11 • h

h = 8 ft

A = 88 ft²

h

h = 12 m2

Find the height of the trapezoid.6.5 m

11.5 m

A = 108 m²

h

How would you find the unknown base?

SOLUTION

A = 12 h(b1 + b2)

b2 = 15 m

12 (8)(9 + b2)96 =

15 = b2

96 = 4(9 + b2)

24 = 9 + b2

Practice:Area of Trapezoids Worksheet