6th Grade Math Textbook, Fundamentals

Lesson 10-6 for exercise sets. Chapter 10 283

Practice & Activities

Find the area of the parallelogram for the given dimensions (bbase and hheight).

1.b400 in.; h330 in. 2.b17 ft; h100 ft 3.b16.65 m; h15.30 m

Find the unknown measurement in the parallelogram (Aarea; bbase; and hheight).

4.A841 mm^2 ; b29 mm 5.A132 ft^2 ; h12 ft

6.A195,325 mi^2 ; h300 mi 7.A54.02 m^2 ; b14.6 m

8.Discuss and Write If the base and height of a parallelogram were halved, how

would its new area compare with its original area? Use an example to explain.

1

2

1

4

A parallelogram has a base of 2.5 cm and a height of 6 cm.

What would happen to the area of the parallelogram if its height were tripled?

• First, find the area of the original figure.
  Abh
  2.5 cm • 6 cm
  15 cm^2

So the area of the new parallelogram would be three

times the area of the original parallelogram.

What would happen to the area of the original

parallelogram if bothits height and its base

were tripled?

New base: 2.5 cm • 3 7.5 cm

New height: 6 cm • 3 18 cm

Abh

7.5 cm • 18 cm

135 cm^2

The new area would be 9 times the original area (15 cm^2 • 9 135 cm^2 ).

If you know the area of a parallelogram and either the base or the height,

you can use the area formula to find the unknown dimension.

A wall hanging in the shape of a parallelogram has an area of 206.25 in.^2 and

a base that measures 8.25 inches. The space for the hanging is 2 feet high.

Will the wall hanging fit in the space?

Abh Use the formula for the area of a parallelogram.

206.258.25h Substitute the known values.

 Divide both sides by 8.25 to isolate h.

25 h Simplify.

The hanging has a height of 25 inches. The space is 2 feet, or 24 inches, tall.

So the hanging will not fit because 2 ft 25 in.

8.25h

8.25

206.25

8.25

• Then find the area of the new figure.
  New height: 6 cm • 3 18 cm
  Abh
  2.5 cm • 18 cm
  45 cm^2
  Key Concept
  Changing Dimensions
  If you multiply either the base or the height
  of a parallelogram by a number n, the new
  area will be ntimes the area of the original.
  If you multiply boththe base and the height
  of the parallelogram by n, the new area will
  be n^2 times the area of the original.