Area and perimeter

A free preview from the Athena Learning Library — the same lesson registered students learn from.

In this lesson: Calculate areas and perimeters of rectangles and squares, solve inverse and two-step problems, and count covering tiles.

Before you start

Tiles cover a floor; a fence goes around a garden. Covering a surface and going around its edge are two different jobs — that is the whole difference between area and perimeter.

Watch it happen

Cover it, then walk around it

A rectangle 8 centimetres long and 12 centimetres wide, shown empty, covered by centimetre squares, and with its edges highlighted.

A rectangle 8 cm long and 12 cm wide. Two different questions can be asked about it: how much surface it covers (area), and how far it is around the edge (perimeter). Keep them apart.

Step 1 of 4

The idea

Perimeter and area measure different things. The perimeter is the distance all the way around the edge of a shape, so you add up the lengths of its sides. It is measured in cm, m or km. The area is the amount of surface inside the shape, so it is measured in square units such as cm² or m².

For a rectangle, the perimeter can be found quickly by adding the length and the width, then doubling the result, because opposite sides are equal. The area is found by multiplying the length by the width. For a square, all four sides are equal, so the perimeter is four times one side, and the area is one side multiplied by itself.

Some questions work backwards. If you know the area and one side, divide the area by that side to find the other side. If a floor is covered by tiles, work out how many tiles fit along each edge and multiply those two numbers together.

Worked example

The rectangle in the pictures is 11 cm long and 6 cm wide. What is its area?

A rectangle 11 centimetres long and 6 centimetres wide, marked out in centimetre squares.

Cover the rectangle with centimetre squares. The first row holds 11 squares — one for each centimetre of length.
There are 6 rows altogether. Counting in rows: 11 × 6 = 66 squares, so the area is 66 cm². (Half-way you had 3 rows filled: 3 × 11 = 33.)
Do not confuse area with perimeter: the perimeter walks the edge, 11 + 6 + 11 + 6 = 34 cm. Area counts the squares inside and is measured in cm².

Answer: 66 cm² — area = length × width = 11 × 6 = 66 cm².

Try one yourself

A different rectangle has an area of 66 cm² and a width of 6 cm. What is its length?

A rectangle marked out in centimetre squares, 6 centimetres wide.

Watch out

Adding the length and width only once for the perimeter — remember to double it, or add all four sides.
Writing area in cm instead of cm² — area is always measured in square units.
Multiplying for the perimeter or adding for the area — check whether the question asks for the edge or the surface.

Quick check

Try these on your own first — then reveal each answer.

1. What is the perimeter of a rectangle 4 cm by 7 cm?

A rectangle 4 centimetres by 7 centimetres with its edges highlighted.

2. What is the area of a rectangle 8 cm by 12 cm?

A rectangle 8 centimetres by 12 centimetres covered in centimetre squares.

Practise this concept

Reading is the first step — the concept sticks when your child answers questions on it. Registered students practise graded questions for this lesson, with instant marking and worked explanations, and the lesson is marked complete in their progress.

Create a free account to practise Sign in