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.
Formulae
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.
Area of a square
$A=x^2$
 $A$
 The Area of the square.  $x$
 The length of a side. 

Example 1
Find the area of the square.
$length = 3m$
$Area = x^2 \\Area = 3^2 \\\underline{Area = 9 m^2} $
Area of a rectangle
$A=l \times w$
 $A$
 The Area of the rectangle.  $l$
 The length of the rectangle.  $w$
 The width of the rectangle. 

Example 2
Find the area of the rectangle.
$length = 3cm, \ width = 5cm\\Area = l \times w \\Area = 3 \times 5 \\\underline{Area = 15c m^2}$
Area of a parallelogram
$A=b \times h$
 $A$
 The Area of the parallelogram.  $b$
 The length of the base of the parallelogram.  $h$
 The perpendicular height of the parallelogram. 

Example 3
Find the area of the parallelogram.
$base = 6m, \ height = 3m \\Area = b \times h \\Area = 6 \times 3 \\\underline{Area = 18 m^2}$
Area of a triangle
$A= \dfrac{1}{2} \times b \times h$
 $A$
 The Area of the triangle.  $b$
 The length of the base of the triangle.  $h$
 The height of the triangle. 

Example 4
Find the area of the triangle.
$base = 6cm, height = 4cm \\Area = \dfrac{1}{2} \times \ b \times \ h \\$
$Area= \dfrac{1}{2} \times 6 \times 4 \\ Area = \dfrac{24}{2} \\ \underline{Area = 12cm^2}$
Volume of a cube
$V=x^3$
 $V$
 The Volume of the cube.  $x$
 The length of a cube. 

Example 5
Find the volume of the cube.
$length = 2cm \\Volume = x^3 \\Volume = 2^3 \\\underline{Volume = 8cm^3}$
Volume of a cuboid
$V=l \times w \times h$
 $V$
 The Volume of the cuboid.  $l$
 The length of the cuboid.  $w$
 The width of the cuboid.  $h$
 The height of the cuboid. 

Example 6
Find the volume of the cuboid.
$height = 3cm, \ width = 5cm, \ length = 2cm$
Substitute the values for height, width and length in to the formula.
$Volume = l \times w \times h \\Volume = 2 \times 5 \times 3 \\\underline{Volume = 30cm^3}$