Area and Perimeter Explained for Kids and Parents

Area and perimeter are taught close together and use the same numbers, so children mix them up all the time. One is a walk round the edge and the other is the carpet in the middle. Keeping those two pictures apart is most of the work. The sums themselves are adding for perimeter and times tables for area.

What is perimeter?

Perimeter is the total distance round the outside of a shape. Picture an ant walking along every side until it is back where it started: the length of the walk is the perimeter. You find it by adding the sides. A triangle with sides of 3 cm, 4 cm and 5 cm has a perimeter of 3 + 4 + 5 = 12 cm. The answer is a length, so it is in ordinary units: cm, m or km.

What is area?

Area is the amount of flat space inside a shape. It is measured by how many squares cover it. A square with sides of 1 cm is one square centimetre, written 1 cm². If 15 of those squares fit inside a rectangle, its area is 15 cm². Younger children find area by counting squares on a grid before they meet any formula.

How do you work out the perimeter and area of a rectangle?

Take a rectangle 5 cm wide and 3 cm high.

• Perimeter: two widths and two heights. 5 + 3 + 5 + 3 = 16 cm, or 2 × (5 + 3) = 16 cm.
• Area: width × height. The rectangle holds 3 rows of 5 squares, so 5 × 3 = 15 cm².

That "rows of squares" picture is the same one used to teach multiplication. The area model in the multiplication visualiser draws any times table fact as a rectangle, and turning the rectangle on its side shows why 3 × 5 and 5 × 3 give the same area. A square is a rectangle with equal sides, so its area is side × side and its perimeter is 4 × side.

What are the formulas for other shapes?

Shape	Perimeter	Area
Square (side s)	4 × s	s × s
Rectangle (width w, height h)	2 × (w + h)	w × h
Triangle (base b, height h)	add the three sides	b × h ÷ 2
Regular pentagon or hexagon (side s)	5 × s or 6 × s	taught later
Circle (radius r)	2 × π × r (the circumference)	π × r × r

A triangle is half of a rectangle with the same base and height, which is where the "÷ 2" comes from. The circle formulas come in secondary school. The diameter is the distance straight across the middle, twice the radius, and the circumference is a little more than 3 diameters. On the 2D shapes page you can change the size of each shape and watch the perimeter, the area and the formula update.

Why do children mix up area and perimeter?

• Same numbers, different sums: both use the width and the height. Ask "round the edge, or inside?" before any working.
• Forgetting two of the sides: a rectangle labelled 5 and 3 has four sides. Children often answer 8, not 16.
• The wrong units: perimeter is in cm, area in cm². The small 2 means squares, not "times 2".
• Thinking the same area means the same perimeter: a 6 by 4 rectangle and a 12 by 2 rectangle have the same area, 24, but perimeters of 20 and 28.

How can you practise area and perimeter at home?

• Draw rectangles on squared paper. Count the squares inside, then check with a multiplication.
• Measure a table top or a book: walk a finger round the edge for perimeter, cover it with sticky notes for area.
• Give 12 squares of paper and ask for every rectangle they can make. Each has an area of 12 but a different perimeter, and the side lengths are the factor pairs of 12.
• Use the 2D shapes and formulas tool to test a guess before working it out.

Area questions get slow when the multiplication is slow, so a few minutes of times table practice helps more than extra geometry. For bigger rectangles, such as 23 by 14, children need long multiplication. When they move on to solid shapes, the same idea becomes surface area: see 3D shapes, faces, edges and vertices for nets, and the shapes hub for both explorers.