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

Perimeter of a rectangle
To find the perimeter of a rectangle use the formula Perimeter = 2 x Length + 2 x Width. So if the length is 12in and the width is 5in then you would multiply 2 x 12in which would give you 24in and then multiply 2 x 5in which would give you 10in, now add 24in + 10in and your answer is 34in. So the perimeter of the triangle is 34in.
Perimeter = 2 x Length + 2 x Width

24 = 2 x 12in and 2 x 5in = 10in

24in + 10in = 36in

Perimeter of a triangle
To find the perimeter of a triangle use the formula Perimeter = Side ₁ + Side ₂ + Side ₃. So if side₁ is 8in, side ₂ is 3in, and side ₃ is 5in then you would add 8in + 3in + 5in and that would give you 16in.
Perimeter = Side ₁ + Side ₂ + Side ₃
16in = 8in + 3in + 5in

Volume Formulas

Volume of a cube
To find the volume of a cube use the formula . Volume = edge ³ So if the edge is 7ft you would multiply 7ft x 7ft x 7ft which would equal 343ft. So the volume of the cube is 343ft.
Volume = edge³
343 = 7ft x 7ft x 7ft

Volume of a rectangular container
To find the volume of a rectangular container use the formula Volume = Length x Width x Height. We’ll make the length 3in, width 6in, and the height 4in. So we need to multiply 3in x 6in x 4in which would equal 72in. The volume of the rectangular container is 72in.
Volume = Length x Width x Height
72in = 3in x 6in x 4in

Volume of a cylinder
To find the volume of a cylinder use the formula Volume = pie x radius² x height. Note: that pie equals 3.14. So if the radius is 3in and the height is 5in you would multiply 3.14 x 3² x 5in. You must do the radius first, so 3 x 3 = 9. Now you can multiply out the problem, 3.14 x 9in x 5in = 141.3

These are the formulas that you will use the most. Memorize these formulas and you shouldn’t have any problems.