Basic Mathematics for College Students

826 Chapter 9 An Introduction to Geometry

SECTION 9.7 Perimeters and Areas of Polygons

The perimeterof a polygon is the distance around it.

DEFINITIONS AND CONCEPTS EXAMPLES

Find the perimeter of the triangle shown below.

Figure Perimeter Formula

Square

Rectangle

Triangle Pabc

P 2 l 2 w

P 4 s

This is the formula for the perimeter of a triangle.

Substitute 11 for a,16 for b,and 23 for c.

Do the addition.

The perimeter of the triangle is 50 inches.

 50

P 11  16  23

Pabc

11 in.

16 in.

23 in.

62. Refer to isosceles trapezoid below. Find
    each measure.
    a.
    b.
    c. m(CB)

m(C)

m(B)

ABCD 63. Find the sum of the angle measures of an octagon.

64. The sum of the measures of the angles of a polygon
    is 3,240°. Find the number of sides the polygon has.

65°

115°

4 yd

7 yd

3 yd

A B

DC

This is the formula for the area of a triangle.

Substitute 5 for b,the length of the base,

and 3 for h,the height. Note that the side

length 7 m is not used in the calculation.

Write 5 as and 3 as.

Multiply the numerators.

Multiply the denominators.

Do the division.

The area of the triangle is 7.5 m^2.

7.5



15

2

3

1

5

 1

1

2

a

5

1

ba

3

1

b

A

1

2

( 5 )( 3 )

A

1

2

bh

Figure Area Formulas

Square

Rectangle

Parallelogram

Triangle

Trapezoid A^12 h(b 1 b 2 )

A^12 bh

Abh

Alw

As^2

5 m

7 m

3 m

The areaof a polygon is the measure of the amount

of surface it encloses.

Find the area of the triangle shown here.