ExerciseSimplify s + s + s + s.

4s

Simplify l + w + l + w.

2l + 2w

Exercise

Solve 22 = 7p.

p = 3 ≈ 3.1417

Exercise

Solve 4s = 84.

s = 21

Exercise

Solve 33 + 2w = 45.

w = 6

Exercise

perimeter—distance around a plane geometric figure

Perimeter Formulas for PolygonsTriangle

a

b

c

p = a + b + c

Perimeter Formulas for PolygonsRectangle

p = 2l + 2wl

w

Perimeter Formulas for Polygons

Square

p = 4s

s

Perimeter Formulas for Polygons

Parallelogram

p = 2a + 2ba

b

Perimeter Formulas for PolygonsTrapezoid

p = a + b + c + d

a c

b

d

Find the perimeter of the polygon.

4 m 5 m

7 mp = 4 + 5 + 7 = 16 m

Example 1

Find the perimeter of the polygon.

5 ft. 5 ft.

12 ft.p = 5 + 12 + 5 + 6 = 28 ft.

6 ft.

Example 1

A parallelogram has a perimeter of 30 in. and a side of 6.5 in. Find the length of the other parallel sides.

Example 2

2a + 2b = p

b = 8.5

2(6.5) + 2b = 3013 + 2b = 30

13 + 2b – 13 = 30 – 132b = 172 2

What is the perimeter of a square if the length of a side is 12?

48

Example

What is the length of a side of a square if its perimeter is 88?

22

Example

What is the length of a diagonal of a square if the length of a side is 12?

12 √ 2 ≈ 17

Example

What is the length of a side of a square if the length of a diagonal is 25.5?

18

Example

What is the perimeter of a regular decagon if the length of a side is 14.5?

145

Example

What is the length of a side of a regular decagon if its perimeter is 167?

16.7

Example

A circle is the set of points in a plane that are equidistant from a fixed point called the center.

Circle

ChordA chord is a line segment with both endpoints on a circle. BC and AD are chords.

BA

CD

EO

DiameterA diameter (d) is a chord passing through the center of

a circle. The chord AD is a diameter of circle O.B

ACD

EO

RadiusA radius is a line segment from the center of a circle to a point on the circle.

BA

CD

EO

OA, OD, and OE are radii of circle O.

circumference—distance around a circle

Circumference Formula for Circles

c = πd

c = 2πr

The circumference is equal to π times

the diameter.The circumference

is equal to two times π times the

radius.

Find the circumference of a circle with a radius of 5.3 cm. Round to the nearest tenth.

= 33.3 cm

c = 2πr= 2π(5.3) = 10.6π= 10.6(3.14)= 33.284

Example 3

Find the circumference of a circle with a diameter of 8 ft. Round to the nearest tenth.

= 25.1 ft.

c = πd= π(8) = 8π= 8(3.14)= 25.12

Example 3

Find the diameter and radius of a circle with a circumference of 30 in. Round to the nearest tenth of an inch.

d ≈ 9.6 in.πd = c3.14d = 303.14 3.14 r = d

2 = 4.8 in.

Example 4

What is the circumference (to the nearest tenth) of a circle if its radius is 12?

75.4

Example

What is the circumference (to the nearest tenth) of a circle if its diameter is 20?

62.8

Example

What is the radius (to the nearest tenth) of a circle if its circumference is 112?

17.8

Example

What are the dimensions of a rectangle whose perimeter is 32 and whose longer side is three times the length of its shorter side?

4 by 12

Example

What are the dimensions of a triangle whose perimeter is 30 and whose sides are in the proportion 1 : 2 : 3?

5, 10, and 15

Example