Geometry Chapter 1.7 Introduction to Perimeter, Circumference, and Area
I) Vocabulary and Formulas:
Notation:
A = Area
P = Perimeter
A) Triangle:
A = (1/2)(base)(height)
P = (side a) + (side b) + (side c)
Example: Given Triangle ABC with side a = 10, b = 17 and c = 21 and the height of the triangle is 8. Find the area and the perimeter.
Area = (1/2)(21)(8) = 84 square units.
Perimeter = 10 + 17 + 21 = 48 units
B) Square: has all the sides equal so the base = height so we will call them all sides.
A = (side)(side) = s2
P = side + side + side + side = 4s
Example: let one side of a square is equal to 5 inches. what is the area and perimeter?
A = (5)2 = 25 square inches
P = 4 (5) = 20 inches
C) Rectangle:
A = (base)(height)
P = 2b + 2h
Example: let the base = 3 and the height = 4
A = (3)(4) = 12 square units
P = (2)(3) + (2)(4) = 6 + 8 = 14 units
D) Circle: 2 radius = diameter
A = π r2
P = Circumference = 2 π r
Example: If a circles diameter is 20 cm, what is the area and circumference?
A = π (10)2 = 100π square cm.
C = (2) π (10) = 20 π cm.
