### Perimeter

A flat shape’s **perimeter** is the **length around all of its sides**.

If you know the length of all of a shape’s sides you can simply **add them together** and find the perimeter.

In some questions you may have to **measure** the sides of the shape with a ruler and then add them up.

Sometimes you are only given some of the lengths, but you can work out the length of the **missing sides** using the information you are given.

Example 1

**Question**: Find the perimeter of this shape:

First we must work out the **length** of each of the sides as some are missing.

They are quite easy to work out from the lengths we are given.

We know that the left side of the shape is 5 cm and that the right side is 3 cm. So the missing value of the cutout must be the difference between these:

5 – 3 = 2 cm.

This is the same for the top and bottom sides, they measure 5 cm and 3 cm, so the missing side is again 2 cm. So we can fill in the missing sides:

Now that we know the length of every side we just **add them up**. When writing out the addition sum it is a good idea to start at a corner of the shape and work your way around the shape listing the length of each side, making sure not to miss one out, until you get back to the corner you started at:

5 + 3 + 2 + 2 + 3 + 5 = **20 cm**

Example 2

**Question**: What is the perimeter of a square with one side 10 cm long?

To answer this question we must know that squares have four sides of equal lengths. Then it is easy, we just add up the four 10 cm long sides to find the perimeter:

10 + 10 + 10 + 10 = **40 cm**

### Area

A shape’s **area** is the amount of **space** it covers.

Area is measured in unit²

For example centimeters squared (cm²)

Or meters squared (m²)

## Squares and Rectangles

To work out the **area of a square or rectangle** you must **multiply it’s width by it’s height**.

Have a look at this **square**:

It has been divided in to a grid showing **smaller squares** that are **1 cm by 1 cm**. The **area** of these little squares is:

1 cm x 1 cm = **1 cm²**

The **big square** has **9** of these little 1cm² squares in it, so it’s area is **9 cm²**.

If the little squares were not drawn in you can calculate the big square’s area by **mutiplying it’s width by it’s height**:

3 cm x 3 cm = **9 cm²**

## Triangles

To work out the **area of a triangle** you must **multiply** x width x height.

Here is a triangle with it’s **width and height** shown:

The **area** of this triangle is:

x 5 cm x 10 cm.

I’m going to work out the 5 x 10 bit first:

5 x 10 = 50

Next we just find half of 50:

50 ÷ 2 = **25 cm²**

## Parallelograms

The area of a parallelogram is **width x perpendicular height**.

The **perpendicular height** is the height in a straight vertical line from the bottom of the shape to the top.

Parallelograms have **two pairs of parallel sides of equal length**.

Here is a parallelogram with it’s width and perpendicular height shown:

The **area** of this parallelogram is:

5 cm x 4 cm = 20 cm²