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
â€‹$A=x^2$â€‹â€‹
 â€‹$A$â€‹â€‹
 The Area of the square.  â€‹$x$â€‹â€‹
 The length of a side. 

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Example 1
Find the area of the square.
 â€‹$3m$â€‹â€‹

â€‹$3m$â€‹â€‹
 
â€‹$length = 3m$â€‹â€‹
â€‹$Area = x^2 \\Area = 3^2 \\\underline{Area = 9 m^2} â€‹$â€‹â€‹
â€‹Area of a rectangle
â€‹$A=l \times w$â€‹â€‹
 â€‹$A$â€‹â€‹
 The Area of the rectangle.  â€‹$l$â€‹â€‹
 The length of the rectangle.  â€‹$w$â€‹â€‹
 The width of the rectangle. 

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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
â€‹$A=b \times h$â€‹â€‹
 â€‹$A$â€‹â€‹
 The Area of the parallelogram.  â€‹$b$
 The length of the base of the parallelogram.  â€‹$h$â€‹â€‹
 The perpendicular height of the parallelogram. 

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Example 3
Find the area of the parallelogram.
â€‹$3m$â€‹â€‹
 
 â€‹$6m$â€‹â€‹

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

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

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

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