Area & perimeter

How many metres of fence do you need for the vegetable patch? Will the carpet fit your room? As soon as space and edges are involved, you are right in the middle of area and perimeter. The two sound similar but answer very different questions, and that is exactly what we will explore now.

Once around the outside, once filled in

The perimeter is the path once around the outside of the shape. Picture an ant walking along the edge: the distance it covers is the perimeter. The area, on the other hand, tells you how much space the shape fills. You can think of it as the number of little unit squares that fit exactly inside the shape. A square with sides of 1 cm has an area of 1 cm².

The formulas for the rectangle

For a rectangle with sides a and b you do not have to count the squares one by one: there are a rows with b squares each, so A = a × b. For the perimeter you walk along both sides twice: P = 2 × (a + b). The square is a special case where all sides are equally long: A = a × a = a² and P = 4 × a. So a rectangle with a = 5 cm and b = 3 cm has A = 15 cm² and P = 16 cm.

Units and composite shapes

Keep an eye on the units: lengths and perimeters are measured in cm or m, areas in cm² or m², because you are counting squares. When you multiply two lengths, both have to be in the same unit, otherwise convert first. If a price per square metre is given, you simply multiply the area by it: 12 m² of carpet at 8 euros per m² costs 96 euros. And what if a shape does not look like a rectangle? Many shapes can be split into rectangles: work out each part separately and add them up at the end. That is how you crack tricky floor plans too.