# Guide to Understanding Geometry Formulas

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 = Side^{2}. 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 = Side ^{2}**

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 side_{1} 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 = edge ^{3}**

^{}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 radius^{2} 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 3^{2} 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.