This document discusses how to calculate the area of parallelograms. It defines key terms like base, height, and parallelogram. The area of a parallelogram is calculated as the base multiplied by the perpendicular height. Examples are provided to demonstrate calculating the area or finding the missing value given the area. The document also briefly discusses rhombuses, noting they are a type of parallelogram with four equal sides and their area is calculated the same way.

1. Area of Parallelograms

2. Goal
Find the area of parallelograms.

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

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

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

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

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

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

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

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

14. Find the Area of a ParallelogramExample 1
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 a ParallelogramExample 2
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.
3.
2.
1.
ANSWER 96 yd2
ANSWER 77 mm2
ANSWER 196 ft2

17. Your Turn:
In Exercises 4–6, A gives the area of the parallelogram.
Find the missing measure.
ANSWER h = 6 in.
ANSWER b = 6 m
ANSWER h = 4 cm
4. A = 72 in.2
5. A = 30 m2
6. A = 28 cm2

18. Rhombus
A parallelogram with opposite equal acute
and obtuse angles and four equal sides.
Diagonals
Diagonals
4 equal sides

19. Area of a Rhombus
Same as Area of parallelogram
A = b . h
b
h