Perimeter & Area
Calculating the perimeter and area of rectangles, triangles, parallelograms and compound shapes.
What is Perimeter & Area?
Perimeter is the total distance around the outside of a shape. Area is the amount of space inside a shape. These are two of the most commonly tested measurement topics in the 11+ exam.
You need to know the formulae for rectangles, triangles and parallelograms, and be able to split compound shapes into simpler shapes to find their areas.
Step-by-Step Method
For perimeter, add up all the sides
Walk around the outside of the shape and add every side length. For a rectangle: P = 2(l + w).
For area of a rectangle: length x width
A = l x w. Make sure both measurements are in the same units.
For area of a triangle: base x height / 2
A = (b x h) / 2. The height must be perpendicular (at right angles) to the base.
For compound shapes, split into rectangles and triangles
Break the shape into simpler shapes, find each area separately, then add them together.
Use the correct units
Perimeter is measured in cm, m etc. Area is measured in cm squared, m squared etc.
Worked Examples
Find the perimeter of a rectangle 12cm by 5cm.
Working
- P = 2(l + w).
- P = 2(12 + 5) = 2 x 17 = 34cm.
Find the area of a triangle with base 8cm and height 6cm.
Working
- A = (b x h) / 2.
- A = (8 x 6) / 2 = 48 / 2 = 24cm squared.
An L-shape is made from a 10cm x 4cm rectangle with a 3cm x 4cm rectangle removed. Find the area.
Working
- Full rectangle area: 10 x 4 = 40 cm squared.
- Removed piece: 3 x 4 = 12 cm squared.
- 40 – 12 = 28 cm squared.
Common Mistakes
Confusing perimeter (distance around) with area (space inside).
Perimeter is a length (cm). Area is a space (cm squared). Think: fence around (perimeter) vs carpet inside (area).
Forgetting to halve for the triangle area formula.
A triangle is half a rectangle. Always remember to divide by 2.
Using the slant height instead of the perpendicular height.
The height must be at right angles to the base. Look for the dashed line or right-angle symbol.
Top Tips
- For perimeter of a rectangle, a quick formula is 2(l + w) – add the two different sides and double.
- For compound shapes, there is often more than one way to split them up. Choose the way that looks simplest.
- If a question gives you the area and asks for a missing side, rearrange the formula.
- Always include units in your answer and make sure they are the right type (cm for perimeter, cm squared for area).
Ready to practise?
Put these techniques into action with our free practice papers.
Practise Maths Questions