Formulae for the area and volume of shapes

In a nutshell

An easy way to work out the area or volume of a shape is by substituting in the relative numbers into a formula.

Below is a list of formulae you need to be able to use to work out the area and volume of simple shapes. For each shape an example has been given.

A=x^2

$A$	The Area of the square.
$x$	The length of a side.

Find the area of the square.

$length = 3m$

$Area = x^2 \\Area = 3^2 \\\underline{Area = 9 m^2} $

A=l \times w

Find the area of the rectangle.

$length = 3cm, \ width = 5cm\\Area = l \times w \\Area = 3 \times 5 \\\underline{Area = 15c m^2}$

A=b \times h

$A$	The Area of the parallelogram.
$b$	The length of the base of the parallelogram.
$h$	The perpendicular height of the parallelogram.

Find the area of the parallelogram.

$base = 6m, \ height = 3m \\Area = b \times h \\Area = 6 \times 3 \\\underline{Area = 18 m^2}$

A= \dfrac{1}{2} \times b \times h

$A$	The Area of the triangle.
$b$	The length of the base of the triangle.
$h$	The height of the triangle.

Find the area of the triangle.

$base = 6cm, height = 4cm \\Area = \dfrac{1}{2} \times \ b \times \ h \\$

$Area= \dfrac{1}{2} \times 6 \times 4 \\ Area = \dfrac{24}{2} \\ \underline{Area = 12cm^2}$

V=x^3

$V$	The Volume of the cube.
$x$	The length of a cube.

Find the volume of the cube.

$length = 2cm \\Volume = x^3 \\Volume = 2^3 \\\underline{Volume = 8cm^3}$

V=l \times w \times h

Find the volume of the cuboid.

$height = 3cm, \ width = 5cm, \ length = 2cm$

Substitute the values for height, width and length in to the formula.

$Volume = l \times w \times h \\Volume = 2 \times 5 \times 3 \\\underline{Volume = 30cm^3}$