Maths Help UK

Area and perimeter word problems

Compound shapes, missing sides, area-vs-perimeter trade-offs.

11+ favourites: an L-shape with one or two missing sides; comparing the area of two rectangles with the same perimeter; carpet/paint quantities.

Worked examples
L-shape with sides 8, 6, 5, 3, 3, 3 (units cm). Area = 8×3 + 5×3 = 39 cm².
Same perimeter, different shape: 4×6 area 24, 5×5 area 25.
Carpet 4m × 5m at £15/m²: cost £300.

Frequently asked questions

Splitting compound shapes?
Pick lines that create rectangles. Add the partial areas.
Missing sides?
Use opposite-side equality (in rectangles, parallel sides equal).