01 — Explanation
How do I find the area of an L-shape or similar rectilinear shape?
Split it into rectangles (the additive method) — draw one internal line, calculate each rectangle's area, then add them together. Any missing side length can usually be found because sides running the same direction must add up to the total: if the full width is m and one section is m, the other is m.
Example: An L-shaped room has total height m, total width m, with a cut-out corner of height m and width m.
- Missing height: m. Missing width: m.
- Split into two rectangles: m² and m².
- Total area: m².
02 — Explanation
When should I subtract instead of add?
Use the subtractive method when the shape is easier to see as a large rectangle with a smaller piece removed — it's often fewer steps than splitting into several positive pieces.
Example: A m m sheet has a cm cm rectangular hole cut from a corner.
- Convert the hole to metres first: cm m, cm m.
- Whole sheet: m². Hole: m².
- Remaining area: m².
Common Misconception: Converting the hole's area using the linear factor (÷100) instead of the area factor (÷10,000). cm² is m², not m² — always convert the side lengths to matching units before multiplying, to sidestep this entirely.
03 — Explanation
How do I handle a compound shape that includes a semicircle?
Treat the semicircle as its own component: find its radius (half of whichever straight edge is the diameter), then use for its area, and add that to the rest of the shape.
Example: A patio is a m m rectangle with a semicircle attached along the m side.
- Radius of semicircle: m.
- Rectangle area: m². Semicircle area: m².
- Total: m² (3 s.f.).
Exam Tip: Keep the semicircle's area as an exact multiple of until the very last step, then add the rectangular part and round only once — this avoids losing accuracy through early rounding.
04 — Explanation
How do I turn a compound area into a total cost?
Multiply the total area by the cost per unit area — but only once every unit matches.
05 — Explanation
What if side lengths are given algebraically?
Treat the missing-length deduction exactly as you would with numbers, just using expressions — sides running in the same direction must still sum to the total, which sets up a mini equation to solve.
Example: An L-shape has total width cm, made up of two sections of width and . Since , solving gives , so — the two widths are cm and cm.
Exam Tip: Always sketch the shape and label every known and deduced length directly onto it before calculating any areas — this makes it far easier to spot which pieces you still need and avoids double-counting or missing a section entirely.
06 — Worked example
Worked Example
A garden is a m m rectangle with a triangular flower bed (base m, height m) removed from one corner. Turf costs £4.20 per m². Find the cost of turfing the remaining garden.
- Rectangle area: m².
- Triangle area: m².
- Remaining area: m².
- Cost: .