Area, perimeter and volume
Maths · Key Stage 2 · The School
Fence, carpet, water
Perimeter is the FENCE around a shape — add all the sides, measured in cm. Area is the CARPET covering it — length × width, measured in cm². Volume is the WATER filling it — length × width × height, in cm³. If you can name the fence, the carpet and the water, you will never confuse the three formulas again.
Units tell you which one it is
The little raised number is not decoration: cm means one dimension, cm² means two, cm³ means three. An answer of "24 cm" for an area is wrong even if 24 is the right number, because the unit says you measured a length. Always write the unit — and let the unit check your thinking.
Compound shapes: cut them up
An L-shape is two rectangles. Split it, find each area, add them. Or draw the big rectangle it would be and subtract the missing corner. Both work; pick whichever needs fewer measurements. For the perimeter of an L-shape you cannot cut and add — you must walk the whole outside edge, and the inside corners are where people go wrong.
An L-shape: 10 cm across the top, 4 cm down the right, then 6 cm left, then 3 cm down, then 4 cm left, then 7 cm up. SPLIT IT: a 10 × 4 rectangle is 40 cm², plus a 4 × 3 rectangle is 12 cm², total 52 cm². SUBTRACT INSTEAD: the whole 10 × 7 rectangle is 70 cm², minus the missing 6 × 3 corner which is 18 cm², giving 52 cm². Same answer both ways, which is how you know it is right.