1. ESSENTIAL QUESTION: How do you find the area of parallelograms?
8.5
ESSENTIAL QUESTION:
How do you find the area of parallelograms?

2. VOCABULARY
Either pair of parallel sides of a parallelogram are called the bases of the parallelogram.

3. VOCABULARY
Either pair of parallel sides of a parallelogram are called the bases of the parallelogram.
The shortest distance between the bases of a parallelogram is called the height of a parallelogram.

4. Area of a Parallelogram

6. Find the area of the parallelogram.
Example 1
Find the Area of a Parallelogram
Find the area of the parallelogram.
SOLUTION
Use the formula for the area of a parallelogram.
Substitute 9 for b and 6 for h.
A = bh
Formula for the area of a parallelogram
= (9)(6)
Substitute 9 for b and 6 for h.
= 54
Multiply.
The parallelogram has an area of 54
square meters.
ANSWER

7. Find the height of the parallelogram
Example 2
Find the Height of a Parallelogram
Find the height of the parallelogram
given that its area is 78 square feet.
SOLUTION
A = bh
Formula for the area of a parallelogram
78 = 12h
Substitute 78 for A and 12 for b.
6.5 = h
Divide each side by 12.
The parallelogram has a height of 6.5 feet.
ANSWER

8. Find the area of the parallelogram.
Checkpoint
Area of Parallelograms
Find the area of the parallelogram. 1. 2. 3.
ANSWER
77 mm2
ANSWER
96 yd2
ANSWER
196 ft2

9. Find the area of the parallelogram.
Checkpoint
Area of Parallelograms
Find the area of the parallelogram. 1.
ANSWER
96 yd2 2.
ANSWER
77 mm2 3.
ANSWER
196 ft2 9

10. Checkpoint
Area of Parallelograms
In Exercises 4–6, A gives the area of the parallelogram. Find the missing measure. 4.
A = 72 in.2 5.
A = 30 m2 6.
A = 28 cm2

11. Checkpoint
Area of Parallelograms
In Exercises 4–6, A gives the area of the parallelogram. Find the missing measure. 4.
A = 72 in.2
ANSWER
h = 6 in. 5.
A = 30 m2
ANSWER
b = 6 m 6.
A = 28 cm2
ANSWER
h = 4 cm 11

12. Area of a Rhombus

15. Find the area of the rhombus.
Example 3
Find the Area of a Rhombus
Find the area of the rhombus. a. b.
SOLUTION b.
A = d1d2 2 1
SOLUTION
A = d1d2 2 1 a.
(6 + 6)(9 + 9) = 2 1 2 1
(14)(10) =
(12)(18) = 2 1
= 70
= 108
The area of the rhombus is 70 square inches.
The area of the rhombus
is 108 square inches. 15

16. Find the area of the triangle.1.
ANSWER
49 in.2 2.
ANSWER
168 m2

17. In Exercises 3 and 4, A gives the area of the triangle
In Exercises 3 and 4, A gives the area of the triangle. Find the missing measure. 3.
A = 65 ft2
ANSWER
h = 10 ft 4.
A = 27 cm2
ANSWER
b = 9 cm
A triangular sail of a boat has a base 5 feet long and the sail has an area of 20 square feet. What is the height of the sail? 5.
ANSWER
8 ft

18. Worksheet 8.5A