6th Grade Math Textbook, Fundamentals

(Marvins-Underground-K-12) #1
Changs’ Pool O’Malleys’ Pool

12 yards 12 yards

6 yards 6 yards

282 Chapter 10

10-6


Aw
12 yd • 6 yd
72 yd^2

base  12 yards

height 
6 yards

base

height

base

height

Update your skills. See page 410.

Area of Parallelograms


Objective To use a formula to find the area of a parallelogram• To rename area units
in equivalent forms• To explore the effect of a change in the base or the height on a parallelogram’s
area• To find an unknown base or height given a parallelogram’s area

The Changs and the O’Malleys have swimming pools in their backyards.
Diagrams of the pools are shown below. What are the areas of the two pools?


 is the number of square units that cover a

figure. The Changs’ pool is shaped like a rectangle.
To find its area, use the formula for the area of a
rectangle: Aw, where length and wwidth.

The O’Malleys’ pool is a parallelogram. To
find its area, imagine removing the triangular
region on the left side of the pool and shifting
it right. You can then see that the two pools have
areas that are exactlythe same. The base and
the height remain the same in the imaginary
rectangle as in the parallelogram.

The of a parallelogram is the length of any of its

sides. The is a perpendicular line segment from
a base to the opposite side. The of a parallelogram
is the length of the altitude. To find the height of some
parallelograms, it is necessary to drop a perpendicular
line segment to an extension of the base.

You can use the formula for the
area of a parallelogram to find
the area of the O’Malleys’ pool.

Abh
12 yd • 6 yd
72 yd^2

So the two pools have the same area, 72 yd^2.

altitude
height

base

Area

Key Concept
Area of a Parallelogram
Abh, where bis the base and his the height
The formula for the area of a parallelogram is related to the formula
for the area of a rectangle that has the same length and width as
the base and height of the parallelogram.

Think
1 yd • 1 yd 1 yd^2

3 ft • 3 ft9 ft^2
So the number of square feet is
9 times the number of square yards.

You can rename the area of a figure by finding its

equivalent in different units. For example, since 1 yd 3 ft,
then 1 yd^2 9 ft^2. So to find the area of the Changs’ pool
in square feet, multiply: 72 • 9 648. The area of the
Changs’ pool is 648 ft^2.
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