# Functional Skills: Perimeter

## Functional Skills: Perimeter Revision

**Perimeter**

The **perimeter** of a shape is total length of all the outside edges. Often not all the side lengths will be given, but you will always be able to deduce them using the other side lengths. You could be asked to find the perimeter of simple shapes or harder compound shapes.

There are **2** skills that you need to learn for the perimeter of shapes.

The following topics are referred to in this page.

**Skill 1: Perimeter of Simple Shapes**

**Example:** Below is a **rectangle **with length of 15 cm and a width of 5.5 cm

Calculate the **perimeter **of the rectangle.

**Opposite **sides of a rectangle have the same length.

Therefore, the two missing sides are 15 cm and 5.5 cm.

We can now work out the perimeter:

**Perimeter **=5.5+5.5+15+15=\textcolor{orange}{41 \text{ cm}}

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**Skill 2: Perimeter of Compound Shapes**

Often you will get asked to work out the **perimeter **of shapes similar to the one below, so you will need to use the given measurements to work out the missing measurements.

**Example:** The compound shape below is made up of two **rectangles**.

Calculate the perimeter of the shape ABCDEF

Using the measurements given, we can work out the lengths of DC and ED

DC=6-4=2 cm

ED=7-3=4 cm

**Perimeter** =6+7+2+4+4+3=\textcolor{orange}{26 \text{ cm}}

**Harder Example:**

The compound shape below is made up of an equilateral triangle, a rectangle and a semi-circle.

Calculate the perimeter of the shape to 2 decimal places.

**[3 marks]**

An equilateral triangle has three sides with equal length, so the two missing sides of the triangle have lengths of 5 cm each.

To work out the arc of the semi circle we need to work out the circumference of the full circle and then half this value.

Circumference =\pi d, where d=5 cm

Circumference of semi circle =\pi \times 5 \times \frac{1}{2} =7.85 cm

**Total perimeter** =5+5+8+8+7.85=\textcolor{orange}{33.85 \text{ cm}}

## Functional Skills: Perimeter Example Questions

**Question 1:Â **Calculate the perimeter of the square ABCD shown below.

**[1 mark]**

A square has four sides in equal length, so the perimeter of the square ABCD=4 \times 11=44 cm

**Question 2:Â **Calculate the perimeter of the isosceles triangle ABC shown below.

**[2 marks]**

An isosceles triangle has two sides with equal length.

So the perimeter of the triangle = 8+6.5+6.5=21 cm

**Question 3:Â **Calculate the perimeter of the shape shown below, giving your answer to 2 decimal places.

**[3 marks]**

We know that the shape is \dfrac{3}{4} of a circle as the missing segment of the circle has an angle of 90\degree.

Therefore we need to find \dfrac{3}{4} of the circumference of the original circle.

Circumference = \pi d, where d=2\times5.5=11 cm

Length of arc = \dfrac{3}{4} \times \pi \times11=25.92

Total perimeter of the shape = 25.92+5.5+5.5=36.92 cm

**Question 4:Â **Mr Kane wants to build a fence around his garden, the fence costs Â£11.99 per metre. Using the diagram, work out the cost of Mr Kane putting a fence up around his garden.

**[3 marks]**

We can work out the missing measurements of the garden using the measurements we have already been given.

7.5+5=12.5 m

13-6=7 m

Then add up all the lengths to get the total perimeter:

12.5+7+5+6+7.5+13=51 m

So the total cost = 51\times Â£11.99=Â£611.49

**Question 5: **Below is a regular hexagon ABCDEF. It has a perimeter of 63 cm.

Calculate the length of one side.

**[2 marks]**

ABCDEF is a regular hexagon, therefore it has 6 equal sides. So the length of one of its sides is 63 \div 6=10.5 cm

## Functional Skills: Perimeter Worksheet and Example Questions

### Perimeter L1

FS Level 1NewOfficial PFS### Perimeter L2

FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]

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