Post on 16-Jan-2016
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