Geometry Formulas

Geometry Formulas:    

Perimeter of a rectangle is the total distance around Perimeter =
2(Length) + 2(Width)

P = 2L + 2W
Perimeter of a triangle is the total distance around
Perimeter = side +side + side

P = S+S+S
Circumference is the distance around a circle Circumference = 2(pi)(radius) or pi(diameter)
Area of a rectangle Area = Length(width) A= LW
Area of a circle Area = pi(radius)2
Volume of a rectangular solid Volume = Length(Width)(Height) V=LWH

Examples of the use of Geometry formulas:

Find the perimeter of a parking lot that has a length of 50 yards and a width of 40 yards.

P = 2L + 2W = 2(50) + 2(40)= 180 yards

Find the perimeter of a triangle with sides of 2 inches, 4 inches, and 5 inches.

P = S+S+S = 2+4+5 = 11 inches

Find the area of a rectangular flag that has a length of 7 feet and a width of 2 feet.

A = LW = 7(2) = 14 square feet

Find the circumference and the area of a circle whose radius is 4 cm. Use 3.14 as an approximation of π.

Find the volume of a rectangular box with a length of 5 inches, a width of 6 inches and a height of 7 inches.

V=LWH = 5(6)(7)=210 cubic inches

(The surface area of this prism is calculated in the next example.) Surface Area of a Rectangular Prism formula is A = 2ab + 2bc + 2ac

The surface area of a rectangular prism is the area of the six rectangles that cover it. Think of this like trying to cover a gift box with wrapping paper. The top and bottom are the same, the front and back are the same, and the left and right sides are the same.

The left and right side each have side lengths of a and b, so the surface area of one of them is a*b, two of them would be 2ab. The area of the top or bottom (side lengths a and c) would be a*c, both of them together would be 2ac.
The front and back each have side lengths of b and c. The area of one of them is b*c, two of them would be 2bc.
Example: Find the surface area of the following rectangular prism. where a = 5 inches, b = 6 inches and c = 7 inches

The left and right sides would be a*b = 5*6 = 30
The front and back would be b*c = 6*7 = 42
The bottom (and top) of the box would be a*c = 5*7 = 35

So then the surface area would be

A = 2(30) + 2(42) = 2(35) = 214 square inches or in2


General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 28-Jan-2013