Area & Perimeter

What Your Child Is Learning

Your child is working with two different ways to measure a flat shape. They sound similar, and they both involve shapes, but they measure completely different things.

Area is the amount of space inside a shape. Imagine painting a wall — the area tells you how much paint you need. It's measured in square units, like cm² (square centimetres). The little ² is important: it means "squared," because you're measuring a flat surface, not a straight line.

Perimeter is the total distance around the outside edge of a shape. Imagine walking around the edge of a football pitch — the perimeter tells you how far you'd walk. It's measured in ordinary units like cm or metres, because it's just a length.

These two measurements describe different properties of the same shape. A shape can have a large area but a small perimeter, or vice versa. That's the key idea your child needs to hold onto: area and perimeter are related to the same shape, but they measure different things.

How Schools Teach It Now

The approach in schools today is very hands-on at first, then builds towards formulae. Here's how it typically works.

Step 1: Counting Squares

Students start by drawing shapes on squared paper and literally counting the squares inside. This builds a solid understanding of what area actually means before any formula appears. For perimeter, they count the units along each edge and add them up.

Step 2: Rectangle Formulae

Once counting squares feels natural, students learn the shortcut formulae for rectangles:

The perimeter formula is just a quicker way of saying "add up all four sides." Since a rectangle has two pairs of equal sides, you add the length and width, then double it.

Step 3: Triangle Formula

Triangles come next. The key insight schools teach is that a triangle is exactly half of the rectangle with the same base and the same perpendicular height. So:

The height here must be the perpendicular height — the straight-up distance from the base to the top, not the slanted side. Schools spend real time on this distinction, because it trips up a lot of students.

Step 4: Compound Shapes

Eventually, students tackle L-shapes and other irregular shapes by splitting them into rectangles, working out each area separately, and adding them together. This is a genuinely useful skill — it's how you'd calculate paint needed for a room with alcoves.

Common Mistakes to Watch For

• Mixing up area and perimeter. This is the big one. A child might multiply the sides when they should be adding them (or the other way round). If they're finding perimeter, they're adding up the side lengths. If they're finding area, they're multiplying. It helps to ask: "Are we measuring the space inside, or the distance around the edge?"
• Forgetting the ½ for triangles. Students often calculate base × height and forget to halve the answer. Remind them: a triangle is half a rectangle, so you always halve it.
• Mixing up units: cm vs cm². Perimeter is a length, so the answer is in cm (or m, or km). Area is a surface, so the answer is in cm² (or m²). If your child writes cm when they mean cm², it's worth gently correcting — marks are often lost for this in exams.
• Using the slanted side instead of the perpendicular height. In triangles, the height must go straight up from the base at a right angle. If the triangle is tilted, the height isn't one of the visible sides — it's a line drawn inside (or outside) the triangle.

Try It Together

Once you've worked through that, try a triangle together: a triangle with a base of 6 cm and a perpendicular height of 4 cm.

Let Them Practise

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