1. ESSENTIAL QUESTION: How do you calculate the area of trapezoids?
8.6
ESSENTIAL QUESTION: How do you calculate the area of trapezoids?

2. VOCABULARY
The shortest distance between the bases of a trapezoid is the height of the trapezoid.

4. Area of a Trapezoid

6. Find the area of the trapezoid.
Example 1
Find the Area of a Trapezoid
Find the area of the trapezoid.
SOLUTION
Formula for the area of a triangle
A =
h(b1 + b2) 1 2 = 1 2
(5)(6 + 8)
Substitute 5 for h, 6 for b1, and 8 for b2. = 1 2
(5)(14)
Simplify within parentheses.
= 35
Simplify.
ANSWER
The area of the trapezoid is 35 square inches. 6

7. Find the area of the trapezoid.
Checkpoint
Area of Trapezoids
Find the area of the trapezoid. 1.
ANSWER
63 m2 2.
ANSWER
182 ft2 3.
ANSWER
50 cm2

8. Example 2
Use the Area of a Trapezoid
Find the value of b2 given that the area of the trapezoid is 96 square meters.
SOLUTION
A = 1 2
h(b1 + b2)
Formula for the area of a trapezoid 1 2
(8)(9 + b2)
96 =
Substitute 96 for A, 8 for h, and 9 for b1.
192 = 8(9 + b2)
Multiply each side by 2.
192 = b2
Use the distributive property.
120 = 8b2
Subtract 72 from each side.
15 = b2
Divide each side by 8.
ANSWER
The value of b2 is 15 meters. 8

9. A gives the area of the trapezoid. Find the missing measure.
Checkpoint
Use the Area of a Trapezoid
A gives the area of the trapezoid. Find the missing measure. 4.
A = 77 ft2

10. Checkpoint
Use the Area of a Trapezoid 5.
A = 39 cm2
ANSWER
12 yards

11. Checkpoint
Use the Area of a Trapezoid 5.
A = 39 cm2
ANSWER
12 yards

12. Checkpoint
Use the Area of a Trapezoid 6.
A = 84 in.2
A trapezoid has an area of 294 square yards. Its height is 14 yards and the length of one base is 30 yards. Find the length of the other base. 7.
ANSWER
12 yards

13. Checkpoint
Use the Area of a Trapezoid 6.
A = 84 in.2
A trapezoid has an area of 294 square yards. Its height is 14 yards and the length of one base is 30 yards. Find the length of the other base. 7.
ANSWER
12 yards

14. A gives the area of the trapezoid. Find the missing measure.
Checkpoint
Use the Area of a Trapezoid
A gives the area of the trapezoid. Find the missing measure. 4.
A = 77 ft2
ANSWER
h = 7 ft 5.
A = 39 cm2
ANSWER
b1 = 5 cm 6.
A = 84 in.2
ANSWER
b2 = 8 in.
A trapezoid has an area of 294 square yards. Its height is 14 yards and the length of one base is 30 yards. Find the length of the other base. 7.
ANSWER
12 yards

17. 1.
Find the area of the parallelogram.
ANSWER
72 square units 2.
Find the area of the rhombus.
ANSWER
288 square units 3.
The area of the parallelogram is 27 square meters. Find the height.
ANSWER
9 m 4.
A parallelogram has a height of 8 feet and an area of 96 square feet. Find the base.
ANSWER
12 ft

18. Worksheet 8.6A