How to explain area and perimeter to your child

Explain area and perimeter by giving your child two different jobs. First, trace the distance around a shape's outside edge. That is its perimeter. Then count how much surface the shape covers. That is its area. Keeping the two jobs visible helps the formulas make sense.

Use squared paper and a pencil. If the squares are not actually one centimetre wide, call their sides "one unit" rather than labelling them centimetres.

Understand the idea

Perimeter measures the length of a boundary. Imagine putting ribbon around the edge of a flat card. You need a length of ribbon, measured in units such as centimetres.

Area measures the surface inside that boundary. Imagine covering the card with equal square tiles, leaving no gaps or overlaps. You need a number of square units, such as square centimetres.

Say: "Are we measuring the path around the edge or the space inside? Show me which part you would measure."

A square centimetre is a square with sides one centimetre long. The small raised two in cm² names that unit. It does not mean that you should multiply your final answer by two.

See it worked through

Inside and around a rectangle

Draw a rectangle 4 cm long and 3 cm wide, divided into twelve 1 cm squares.

Trace its four sides. Two sides measure 4 cm and two measure 3 cm. Add every outside side: 4 + 3 + 4 + 3 = 14 cm. The perimeter is 14 cm.

Now count the squares inside. There are three rows of four squares, so 3 × 4 = 12. Each square covers one square centimetre. The area is 12 cm².

Ask: "Why did we add for the edge but multiply for the inside?"

We added the four lengths making the boundary. For the area, multiplication counted equal rows of square units covering the rectangle.

The formula length × width works for a rectangle because its equal rows fit together without gaps. You can also count the squares directly. Internal grid lines help us count area; they are not part of the rectangle's perimeter.

Try it together

Compare two rectangles

Draw a second rectangle 6 cm long and 2 cm wide on a centimetre grid. Ask your child to find its area and perimeter.

Before they calculate, ask whether they think it covers more, less or the same area as the 4 cm by 3 cm rectangle. Then ask whether the distance around its edge will also be the same.

Have them mark the boundary in one colour and shade the inside in another.

Check the answer

The area is 6 × 2 = 12 cm², the same as the first rectangle. Its perimeter is 6 + 2 + 6 + 2 = 16 cm, which is 2 cm greater than the first perimeter. Shapes can cover the same area while having different boundary lengths.

Check their understanding

Ask your child which measurement tells you how much fencing a rectangular garden needs. Perimeter measures the distance around it. Which tells you how much turf covers the garden? Area measures the surface inside.

Then ask them to label the answer units before doing a calculation. Choosing centimetres or square centimetres can prompt them to think about what they are measuring.

Make it easier or harder

Make it easier with a rectangle made from two rows of three square tiles. Count the six tiles for area, then trace and count the ten outside unit-length edges for perimeter.

Make it harder by drawing a 1 cm by 12 cm rectangle. It also has area 12 cm², but its perimeter is 26 cm. Compare all three rectangles and ask your child to explain why stretching the arrangement changes the boundary without adding area.

Teaching notes

NSW Education's area and perimeter investigation explores how changing a shape affects these measurements. The rectangle activities here are original examples that let a child count and compare both quantities.

Numeracy practice

Help your child apply their maths understanding with practice questions and explanations.

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