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Formulae for the area and volume of shapes

Formulae for the area and volume of shapes

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Summary

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=x2A=x^2​​
​AA​​
The Area of the square.
​xx​​
The length of a side.

​

Example 1

Find the area of the square.

Maths; Measurement; KS2 Year 6; Formulae for the area and volume of shapes

​length=3mlength = 3m​​

​Area=x2Area=32Area=9m2‾​Area = x^2 \\Area = 3^2 \\\underline{Area = 9 m^2} ​ ​​


​Area of a rectangle

​A=l×wA=l \times w​​
​AA​​
The Area of the rectangle.
​ll​​
The length of the rectangle.
​ww​​
The width of the rectangle.

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Example 2

Find the area of the rectangle.

Maths; Measurement; KS2 Year 6; Formulae for the area and volume of shapes


length=3cm, width=5cmArea=l×wArea=3×5Area=15cm2‾length = 3cm, \ width = 5cm\\Area = l \times w \\Area = 3 \times 5 \\\underline{Area = 15c m^2}


Area of a parallelogram

​A=b×hA=b \times h​​
​AA​​
The Area of the parallelogram.
​bb
The length of the base of the parallelogram.
​hh​​
The perpendicular height of the parallelogram.

​

Example 3

Find the area of the parallelogram.

base=6m, height=3mArea=b×hArea=6×3Area=18m2‾base = 6m, \ height = 3m \\Area = b \times h \\Area = 6 \times 3 \\\underline{Area = 18 m^2}


​Area of a triangle

​A=12×b×hA= \dfrac{1}{2} \times b \times h​​
​AA​​
The Area of the triangle.
​bb
The length of the base of the triangle.
​hh​​
The height of the triangle.

​

Example 4

Find the area of the triangle.

Maths; Measurement; KS2 Year 6; Formulae for the area and volume of shapes

     base=6cm,height=4cmArea=12× b× hbase = 6cm, height = 4cm \\Area = \dfrac{1}{2} \times \ b \times \ h \\

​​​Area=12×6×4Area=242Area=12cm2‾Area= \dfrac{1}{2} \times 6 \times 4 \\ Area = \dfrac{24}{2} \\ \underline{Area = 12cm^2}​​


Volume of a cube

​V=x3V=x^3​​
​VV​​
The Volume of the cube.
​xx​​
The length of a cube.

​

Example 5

Find the volume of the cube.

Maths; Measurement; KS2 Year 6; Formulae for the area and volume of shapes

​length=2cmVolume=x3Volume=23Volume=8cm3‾length = 2cm \\Volume = x^3 \\Volume = 2^3 \\\underline{Volume = 8cm^3}


Volume of a cuboid

​V=l×w×hV=l \times w \times h​​
​VV​​
The Volume of the cuboid.
​ll​​
The length of the cuboid.
​ww​​
The width of the cuboid.
​hh​​
The height of the cuboid.

​

Example 6

Find the volume of the cuboid.

Maths; Measurement; KS2 Year 6; Formulae for the area and volume of shapes

​height=3cm, width=5cm, length=2cmheight = 3cm, \ width = 5cm, \ length = 2cm​​


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

Volume=l×w×hVolume=2×5×3Volume=30cm3‾Volume = l \times w \times h \\Volume = 2 \times 5 \times 3 \\\underline{Volume = 30cm^3}

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Read more

Learn with Basics

Length:
Length: Comparing, adding and subtracting

Length: Comparing, adding and subtracting

Volume: Comparing, adding and subtracting

Volume: Comparing, adding and subtracting

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Formulae for the area and volume of shapes

Formulae for the area and volume of shapes

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FAQs - Frequently Asked Questions

How do you work out the area of a parallelogram ?

How do you work out the volume of a cube?

How do you work out the volume of a cuboid ?