Basic Mathematics for College Students

Chapter 9 Summary and Review 827

If we know the area of a polygon, we can often use
algebra to find an unknown measurement.

The area of the parallelogram

shown here is 208 ft^2. Find the

height.

26 ft

h

This is the formula for the area of a parallelogram.

Substitute 208 for A,the area, and 26 for b,

the length of the base.

To isolate h,undo the multiplication by 26

by dividing both sides by 26.

Do the division.

The height of the parallelogram is 8 feet.

8 h

208

26



26 h

26

208  26 h

Abh

To find the perimeter or area of a polygon, all the
measurements must be in the same units.If they are
not, use unit conversion factors to change them to the
same unit.

To find the perimeter or area

of the rectangle shown here,

we need to express the length

in inches.

Convert 4 feet to inches using a unit

conversion factor.

Remove the common units of feet in the

numerator and denominator. The unit of

inches remain.

Do the multiplication.

The length of the rectangle is 48 inches. Now we can find the

perimeter (in inches) or area (in in.^2 ) of the rectangle.

48 in.

 4 12 in.

4 ft

4 ft

1



12 in.

1 ft

4 ft

11 in.

To find the area of an irregular shape, break up the
shape into familiar polygons. Find the area of each
polygon, and then add the results.

Find the area of the shaded figure

shown here.

We will find the area of the lower

portion of the figure (the trapezoid)

and the area of the upper portion

(the square) and then add the results.

18 cm

8 cm

8 cm

10 cm

This is the formula for the area of a

trapezoid.

Substitute 8 for b 1 , 18 for b 2 , and

10 for h.

Do the addition within the parentheses.

Do the multiplication.

The area of the trapezoid is 130 cm^2.

This is the formula for the area of a square.

Substitute 8 for s.

Evaluate the exponential expression.

The area of the square is 64 cm^2.

 64

Asquare 82

Asquares^2

 130



1

2

(10)(26)

Atrapezoid

1

2

( 10 )( 8  18 )

Atrapezoid

1

2

h(b 1 b 2 )