# Perimeter of Rhombus

Welcome to our Perimeter of Rhombus support page.

We will explain how to find the perimeter of a rhombus and show you some worked examples.

We also have some worksheets so that you can practice this skill.

## Perimeter of Rhombus support page

### Examples - The Easier Version

Example 1

Find the perimeter of the rhombus below.

The rhombus has sides of length 5cm.

So to work out the perimeter we need to add up the length of all four sides.

4 x 5cm = 20cm

So the rhombus has a perimeter of 20cm.

Example 2

Find the perimeter of shape below.

This rhombus is actually a square, as the angles are all right angles.

To work out the perimeter we need to multiply the length of one side by 4.

So 6cm x 4 = 24cm.

So the rhombus has a perimeter of 24cm.

Example 3

Find the perimeter of shape below.

This rhombus has sides length 3 ½ cm.

To work out the perimeter we need to multiply the length of one side by 4.

So 3 ½ cm x 4 = 14cm.

So the perimeter of the rhombus is 14cm.

Example 4

Find out the length of the sides of this shape.

This rhombus has a perimeter of 32cm and we need to find out the length of the sides.

To work out the perimeter we need to multiply the length of one side by 4.

So 4 x side length = 32cm.

This means that the side length must be 32 ÷ 4 = 8.

So the length of each side of the rhombus is 8cm.

### Examples - The Harder Version

Example 1

Find the perimeter of the rhombus below.

We know the perpendicular width and height of one of the sides so we can use Pythagoras' theorem to find the hypotenuse which is also the side of the rhombus.

Pythagoras' theorem says that the square of the two shorter sides (legs) on a right triangle is equal to the square of the longest side (the hypotenuse).

So if h is the longest side (or hypotenuse), then h2 = 62 + 82.

This gives us h2 = 34 + 64 = 100.

So h=√ 100 = 10cm.

So the length of one of the sides of the rhombus is 10cm, so we need to multiply this length by 4 to give the perimeter.

The perimeter of the rhombus is 4x10 = 40cm.

Example 2

Find the perimeter of the rhombus below correct to 1dp.

Once again, we know the perpendicular width and height of the side, so we can use Pythagoras' theorem to find the length of the side.

Pythagoras' theorem says that the square of the two shorter sides (legs) on a right triangle is equal to the square of the longest side (the hypotenuse).

So if h is the longest side (or hypotenuse), then h2 = 72 + 42.

This gives us h2 = 49 + 16 = 65.

So h=√ 65 cm.

So the length of one of the sides of the rhombus is √65 cm so we need to multiply this length by 4 to give us the perimeter.

The perimeter of the rhombus is 4x √65 = 32.2cm to 1dp.

Example 3

Find the perimeter of the rhombus below.

This time we have been give the total perpendicular width and height of the rhombus.

However, we only need to perpendicular height and width of one side, so we need to halve the measurements.

The perpendicular width of one side is 30cm ÷ 2 = 15cm.

The perpendicular height of one side is 16cm ÷ 2 = 8cm.

So now we have the information we need to help us find the missing side:

Pythagoras' theorem says that the square of the two shorter sides (legs) on a right triangle is equal to the square of the longest side (the hypotenuse).

So if h is the longest side (or hypotenuse), then h2 = 152 + 82.

This gives us h2 = 225 + 64 = 289.

So h=√ 289 = 17cm.

So the length of one of the sides of the rhombus is 17cm so we need to multiply this length by 4 to give us the perimeter.

The perimeter of the rhombus is 4 x 17cm = 68cm.

### More Recommended Math Resources

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### Online Perimeter Practice

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