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Area of a Parallelogram
BEFORE
Now
WHY?
You found the area
of a rectangle.
You’ll find the area
of a parallelogram.
So you can estimate the area of
Lake Erie, as in Example 3.
Finding Areas The base of a parallelogram is the length of any of
Word Watch
base of a parallelogram,
p. 476
height of a parallelogram,
p. 476
perpendicular, p. 476
its sides. The height of a parallelogram is the perpendicular distance
between the side whose length is the base and the opposite side. Two
lines are perpendicular if they meet at a right angle.
height, h
base, b
The area of a parallelogram is the product of the base and the height.
Area of a Parallelogram
Words Area base p height
Algebra
with
Notetaking
EXAMPLE
Include the formula for the
area of a parallelogram in
your notebook. Include an
example like the one
shown in Example 1.
1
h
A bh
b
Finding the Area of a Parallelogram
Find the area of the parallelogram
shown at the right.
2m
5m
Solution
A bh
Write the formula for the area of a parallelogram.
5p2
Substitute 5 for b and 2 for h.
10
Simplify.
ANSWER The area of the parallelogram is 10 square meters.
Your turn now
Find the area of the parallelogram described.
1. base 6 in., height 10 in.
476
Chapter 10
Geometry and Measurement
2. base 7 cm, height 4 cm
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EXAMPLE
2
Finding an Unknown Dimension
The area of a parallelogram is 45 square centimeters and the
height is 9 centimeters. What is the base?
A bh
Write the formula for the area of a parallelogram.
45 b p 9
Substitute 45 for A and 9 for h.
b 45 9
Write a related division equation.
b5
Simplify.
ANSWER The base is 5 centimeters.
EXAMPLE
Geography
3
Estimating Area
Geography A parallelogram
can be used to approximate
the shape of Lake Erie. Use the
map and the scale to estimate
the area of Lake Erie.
m
1c
Detroit
m
4c
Toledo
Cleveland
1 cm : 92 km
Solution
1 Use the scale to find the base, b, and the height, h, in kilometers.
■
Lake Erie
The area of Lake Superior
is about 82,100 square
kilometers. About how many
times as great as the area
of Lake Erie is the area of
Lake Superior?
Base
Height
1 cm
4 cm
92 k m
b km
1 cm
1 cm
92 k m
h km
1 p b 92 p 4
1 p h 92 p 1
b 368
h 92
2 Estimate the area of Lake Erie.
A bh
Write the formula for the area of a parallelogram.
368 p 92
Substitute 368 for b and 92 for h.
33,856
Simplify.
ANSWER The area of Lake Erie is about 33,856 square kilometers.
Your turn now
Find the unknown length.
3. Area of parallelogram 72 in.2, base 12 in., height _?_
4. Area of parallelogram 125 mm2, height 5 mm, base _?_
Lesson 10.1
Area of a Parallelogram
477
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INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 717
Getting Ready to Practice
1. Vocabulary To find the area of a parallelogram, you multiply the _?_ by
the _?_.
Find the area of the parallelogram.
2.
3.
3 ft
10 yd
15 ft
20 yd
4. Tennessee A parallelogram
can be used to approximate
the shape of Tennessee.
Use the scale on the map
to estimate the area of
Tennessee.
Nashville
14 mm
55 mm
1 mm: 14 km
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
5–9, 12
10, 11
15
Find the area of the parallelogram.
5.
6.
10 ft
7m
7 ft
12 m
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
7.
8.
5 in.
6 in.
Rug design (detail)
15 mm
32 mm
Digital art (detail)
9. The height of a parallelogram is 9 meters and the base is 7 meters.
What is the area of the parallelogram?
10. The area of a parallelogram is 54 square inches and the height is
9 inches. What is the base of the parallelogram?
11. The area of a parallelogram is 120 square yards and the base is
12 yards. What is the height of the parallelogram?
478
Chapter 10
Geometry and Measurement
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50.8 mm
12. Tangrams Tangrams are Chinese
Tangrams
puzzle shapes that can be arranged
into pictures, like the one shown at
the right. Find the area of the
parallelogram piece.
25.4 mm
13. Draw 2 different parallelograms
that each have an area of
12 square centimeters.
14. Quilts The base of one parallelogram
in a quilt is 6 inches and the height is
3 inches. About how many of these parallelograms do you need to
cover an area of 7500 square inches?
15. Estimation Estimate
■
Tangrams
The tangram pieces in the
photo can be arranged to
form two congruent squares
that fit into the box. Estimate
the fraction of the total area
of the tangram pieces that is
covered by one large triangle.
the area of Puerto Rico.
Then tell if your estimate
is a high estimate or a
low estimate. Explain
your reasoning.
San Juan
18 mm
Caguas
Ponce
50 mm
2 mm : 8 km
16. Challenge The base of a
parallelogram is 3 inches longer than its height. The height is 7 inches.
What is the area of the parallelogram?
Mixed Review
Solve the equation using mental math. (Lesson 1.6)
17. x 5 12
18. x 12 30
19. 4x 32
20. 6x 72
21. Sketch 2 different figures that have one line of symmetry. (Lesson 9.8)
Basic Skills Find the product.
1
22. p 4
2
1
23. p 12
2
1
24. p 5 p 6
2
1
25. p 12 p 8
2
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
26. Multiple Choice The height of a parallelogram is 36 meters and the
base is 6 meters. What is the area of the parallelogram?
A. 6 m2
B. 30 m2
C. 42 m2
D. 216 m2
27. Multiple Choice A parallelogram has an area of 300 square feet and a
base of 20 feet. What is the height of the parallelogram?
F. 15 ft
G. 15 ft2
H. 6000 ft
Lesson 10.1
I. 6000 ft2
Area of a Parallelogram
479