1. Area of Parallelograms
Section 8.5

2. Goal
Find the area of parallelograms.

3. Key Vocabulary Base of a parallelogram Height of a parallelogram
Rhombus

4. Parallelogram
A parallelogram is a quadrilateral where the opposite sides are congruent and parallel.
A rectangle is a type of parallelogram, but we often see parallelograms that are not rectangles (parallelograms without right angles).

5. The Base of a Parallelogram
Either pair of parallel sides of a parallelogram are called the bases of the parallelogram.
base
base
base
base

6. The Height of a Parallelogram
The shortest distance (perpendicular distance) between the bases of a parallelogram is called the height of the parallelogram.
The height of the parallelogram is always perpendicular to the bases.

7. Area of Parallelogram What is the area of this parallelogram? h=height
b=base

8. Area of Parallelogram What is the area of this parallelogram? h=height
b=base
CUT HERE!

9. Area of Parallelogram What is the area of this parallelogram? h=height
b=base
MOVE TO HERE!

10. the area of this rectangle
Area of Parallelogram
It’s the same as
the area of this rectangle
h=height
b=base

11. Area of Parallelogram Arearectangle= base x height h=height b=base
(perpendicular height h)
h=height
b=base

12. Area of Parallelogram Areaparallelogram = base x height h=height
(perpendicular height h)
h=height
b=base

13. Area of Parallelogram Words: Area =(base)(height) Symbols: A = bh h b
Very Important: The height must be perpendicular to the base.

14. 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

15. 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

16. Your Turn:
Find the area of the parallelogram. 1.
ANSWER
96 yd2 2.
ANSWER
77 mm2 3.
ANSWER
196 ft2

17. Your Turn:
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