Basic Mathematics for College Students

9.7 Perimeters and Areas of Polygons 779

Analyze

• The truss is in the shape of an isosceles triangle. Given


• One of the sides of equal length is 20 feet long. Given


• The perimeter of the truss is 76 feet. Given


• What is the length of the base of the truss? Find

Form an EquationWe can let equal the length of the
base of the truss (in feet). At this stage, it is helpful to draw
a sketch. (See the figure on the right.) If one of the sides of
equal length is 20 feet long, so is the other.
Because 76 linear feet of lumber were used to make the triangular-shaped
truss,

plus plus equals

b  20  20  76

Solve

Combine like terms.

To isolate b,subtract 40 from both sides.

StateThe length of the base of the truss is 36 ft.

CheckIf we add the lengths of the parts of the truss, we get
36 ft20 ft20 ft76 ft. The result checks.

b 36

b 40  76

b 20  20  76

the perimeter

of the truss.

the length

of the

other side

the length

of one side

The length

of the base

of the truss

b

76

 40

36

Using Your CALCULATOR Perimeters of Figures That Are

Combinations of Polygons

To find the perimeter of the figure shown below, we need to know the values of

and. Since the figure is a combination of two rectangles, we can use a

calculator to see that

x y

y cm

x cm

4.75 cm

10.17 cm

12.5 cm

20.25 cm

b

20 20

and

The perimeter of the figure is

We can use a scientific calculator to make this calculation.

20.25 12.5 10.17 4.75 10.08 7.75

The perimeter is 65.5 centimeters.

      65.5

P20.2512.510.174.7510.087.75

P20.2512.510.174.75xy

P

10.08 cm 7.75 cm

x20.2510.17 y12.54.75