Guide to Understanding Geometry Formulas

In Geometry we must use formulas to find the area, perimeter, and volume of certain shapes like circles, triangles, squares, and rectangles for example. Each shape requires a certain formula to find the area, perimeter, and volume. By memorizing these formulas, your life in geometry will be much easier.

So let's take a look at the most common used shapes in geometry and the formulas we must use to find the area, perimeter, and volume. I will list each formula, explain how to do it, and show you an example. Please take a look at the three images to get a graphic look at how to do each one.

Area Formulas

Area of a square
Area of a square is the easiest formula of them all. To find the area of the square use the formula Area = Side². So if you have a square and one side is 6ft, you would multiply 6ft x 6ft which would equal 36. The area of the square would be 36ft.
Area = Side²
36ft   = 6ft x 6ft

Area of a rectangle
To find the area of a rectangle you would use the formula Area = Length x Width. If the length of a rectangle is 8in and the width of the rectangle is 2in, then you would multiply 8 x 2 which would give you 16in.
Area = Length x Width
16in  = 8in x 2in

Area of a triangle
To find the area of a triangle use the formula Area = 1/2 x Base x Height. If the base is is 6in and the height is 4 then you would multiply 6 x 4 x 0.5 which would give you 12.
Area = 1/2 x Base x Height
12    =  0.5 x 6 x 4

Area of a circle
To find the area of a circle use the formula Area = Pie x Radius ². Note: Pie equals 3.14. If the radius is 2in you would multiply 2in x 2in x 3.14 and your answer would be 12.56in and that rounded to the nearest inch would be 13.
Area = Pie x Radius ²
Area = 3.14 x 2 ²
2 x 2 = 4
3.14 x 4 = 12.56

Perimeter Formulas

Perimeter of a square
To find the perimeter of a square use the formula Perimeter = 4 x Side. So if one side is 3ft then you would multiply 4 x 3ft which would equal 12ft. So the perimeter of the square is 12ft.
Perimeter = 4 x Side
   12 = 4 x 3ft