Area & Perimeter

• Perimeter is the total distance around the outside of a 2D shape — just add up every side length.
• The perimeter of a circle has a special name: the circumference.
• Compound shapes (irregular ones) can be split into rectangles, triangles, and parts of circles.
• Use shape properties (equal sides, opposite sides equal, etc.) and sometimes Pythagoras' theorem to find missing lengths before you can find the perimeter.
• Area is the amount of 2D space inside a shape's boundary, measured in squared units (cm², m², etc.).
• You need to know the area formulas for a rectangle, triangle, trapezium, and parallelogram by heart (only the triangle one is given to you in the exam).
• To find the area of a compound shape: split it into standard shapes and add the areas — or sometimes it's easier to complete a bigger shape and subtract the extra bit.
• Problem-solving questions dress area up in real-life contexts (carpets, painting, tiling) — often involving cost and compound units like £/m².

Perimeter is simply the total distance you'd walk if you traced all the way around the outside edge of a 2D shape and ended up back where you started. Because it's a length, it's measured in "one dimension" — units like mm, cm, or m (never squared).

Think of a rectangular garden with a fence around it. The perimeter is the total length of fencing you'd need to buy. It doesn't matter what shape the garden is — you're just measuring the boundary line.

For any regular shape (all sides equal — like a square or equilateral triangle), you don't need to add up every side one by one. Just multiply the number of sides by the length of one side.

A compound shape is made of two or more simpler 2D shapes joined together (like an L-shape, which is really two rectangles pushed together). The strategy is always the same:

1. Look for sides that must be equal — dashes on a diagram, or the question telling you directly, often signal this (e.g. two sides of an isosceles triangle).
2. Use the shape's structure to work out missing lengths. A classic trick: on an L-shape, the sum of the two shorter horizontal (or vertical) sides equals the one long side directly opposite them.
3. Sometimes you'll need Pythagoras' theorem to find a missing side on a right-angled triangle hiding inside the compound shape.
4. Once every side length is known, just add them all up.