In short: To find the area of a compound shape, split it into simple rectangles, work out the area of each one, then add them together. Use the measurements you are given to find any missing lengths first. For an L-shape, two rectangles are usually enough.
Knowing how to find the area of a compound shape is an important GCSE Foundation skill, since exam questions often show floor plans, gardens and L-shaped rooms rather than plain rectangles. The reliable approach is to break the shape into rectangles you already know how to handle. This guide shows the splitting method step by step, with a worked L-shape example you can follow.
The reliable method
A compound shape is just simple shapes joined together, so split it back into those simple parts.
- Split the shape into rectangles by drawing one or two straight lines. An L-shape usually splits into two rectangles.
- Work out any missing lengths. Opposite sides of the whole shape must match, so a missing length is the difference between two known lengths along the same direction.
- Find the area of each rectangle using area = length × width.
- Add the rectangle areas together to get the total area.
- Write the answer in square units, such as square centimetres (cm²).
If it is easier, you can instead find the area of a large complete rectangle and subtract the missing corner. Both methods give the same answer.
A worked example
An L-shaped room is 10 m wide and 8 m tall overall. A rectangular corner measuring 6 m by 5 m is missing from the top right. Find the area of the floor.
We split the L-shape into two rectangles with one horizontal line.
Identify the two rectangles:
- Bottom rectangle: the full width of 10 m, with a height of 3 m (because the total height is 8 m and the upper section is 5 m, so 8 − 5 = 3 m).
- Top-left rectangle: height 5 m, and a width of 4 m (because the total width is 10 m and the missing corner is 6 m, so 10 − 6 = 4 m).
Find each area:
- Bottom rectangle: 10 × 3 = 30 m²
- Top-left rectangle: 4 × 5 = 20 m²
Add them together:
- Total area = 30 + 20 = 50 m²
(Check by subtraction: the full rectangle would be 10 × 8 = 80 m², and the missing corner is 6 × 5 = 30 m², so 80 − 30 = 50 m², which matches.)
This works because the two rectangles cover every part of the L-shape exactly once, with no gaps and no overlap, so their areas simply add up to the whole.
Common mistakes to avoid
- Trap: leaving gaps or overlapping the rectangles. Splitting the shape so part is counted twice or missed. Fix: draw your split line carefully and check every piece of the shape is covered once.
- Trap: using the wrong missing length. Guessing a side instead of subtracting. Fix: opposite sides of the whole shape are equal, so find a missing length by subtracting the known parts.
- Trap: adding lengths instead of multiplying. Working out 10 + 3 rather than 10 × 3 for an area. Fix: area is always length × width, never length + width.
- Trap: confusing area with perimeter. Finding the distance around the edge when the question asks for the space inside. Fix: see [area and perimeter confusion explained](/misconceptions/area-perimeter-conflation).
Frequently asked questions
How do you find the area of an L-shape? Split the L-shape into two rectangles with a single straight line. Work out any missing side lengths by subtracting known lengths, find the area of each rectangle using length × width, then add the two areas together.
What is the formula for the area of a compound shape? There is no single formula. You break the shape into rectangles (or other simple shapes), use area = length × width for each, and add the areas. For shapes with a piece cut out, you can subtract instead.
How do you find a missing length on a compound shape? Use the fact that opposite sides of the whole shape are equal. A missing length along one direction is the total length minus the other known lengths in that same direction. For example, 10 − 6 = 4.
What units should the area be in? Square units, written with a small 2, such as cm² or m². Area measures the space a shape covers, so it always uses squared units, unlike perimeter, which uses ordinary length units.
Can you find a compound area by subtracting? Yes. Work out the area of the smallest complete rectangle that surrounds the shape, then subtract the area of the missing corner. This gives the same answer as splitting and adding.
Practise this
Find out which mistakes cost marks — [take the free diagnostic](/diagnostic). Related: [area and perimeter confusion explained](/misconceptions/area-perimeter-conflation).