1.8: Perimeter, Circumference, and

AreaPart I

Today’s Objectives

Solve for the perimeter or circumference of basic shapes

Use the distance formula to solve for the perimeter of basic shapes

Perimeter of Polygons

Perimeter – the sum of the lengths of a polygon’s sides

l

w

𝑃=2𝑙+2𝑤

a b

c

𝑃=𝑎+𝑏+𝑐

Finding the Perimeter of a Rectangle

What is the perimeter of a 13 by 6 rectangle?

l=13

w=6

𝑃=2(13)+2(6) 𝑃=26+12 𝑃=38

Circumference of a Circle

Circumference – distance around a circle

r

d

𝐶=2𝜋 𝑟

𝐶=𝜋 𝑑

𝑜𝑟

Finding the Circumference of a Circle

What is the circumference of a circle with radius 5?

r = 5

𝐶=2𝜋 𝑟

𝐶=2𝜋 (5)

𝐶=10𝜋

𝐶=10(3.1 4)¿31.4

Perimeter on a Coordinate Plane Find the perimeter of the triangle with vertices A(-3,4), B(1,-2), and

C(5,5).

𝐴𝐵=√ (1−−3 )2+(−2−4 )2

AC

B

¿√ (4 )2+ (−6 )2

¿√16+36 ¿√52¿7.21

𝐵𝐶=√ (5−1 )2+ (5−−2 )2 ¿√ (4 )2+ (7 )2

¿√16+49 ¿√66¿8.12

𝐴𝐶=√ (5−−3 )2+(5−4 )2 ¿√ (8 )2+(1 )2

¿√64+1 ¿√65¿8.06

P = 7.21 + 8.12 +8.06P = 23.39

Circumference on a Coordinate Plane Find the circumference of the circle with a center C(-3,2) and contains

the point A(0,3).

CAr

𝑟=√ (0−−3 )2+(3−2 )2

𝑟=√ (−3 )2+(1 )2

𝑟=√9+1 ¿√10 ≈3.16

𝐶=2𝜋 (3.16) ¿19.84

Take Home Message

Perimeter of polygons

Circumference of circles

The distance formula can be used to solve other problems