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

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Example 1

Find the area of the square.

	​$$3m$$​​
​$$3m$$​​

​$$length = 3m$$​​

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

​Area of a 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

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Example 3

Find the area of the parallelogram.

​$$3m$$​​
	​$$6m$$​​

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

​Area of a triangle

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Example 4

Find the area of the triangle.

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

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

Volume of a cube

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Example 5

Find the volume of the cube.

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

Volume of a cuboid

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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.

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

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