Word based area problems: compound shapes
22 October 2026
When your child faces a word problem about area, it can help to break the question down into simple parts. Compound shapes often look tricky, but if you split them into rectangles and squares, each step becomes much clearer.
Worked example
A playground is made of a rectangle 8 m long and 5 m wide, joined to a square with sides of 3 m. What is the total area of the playground?
First, find the area of the rectangle: 8 × 5 = 40 m².
Next, find the area of the square: 3 × 3 = 9 m².
Now, add the two areas: 40 m² + 9 m² = 49 m².
Key insight: Break the shape into smaller shapes, find each area, then add them together.
The correct answer is 49 m².
After working through this example, your child will know how to find the total area of a compound shape by looking for smaller shapes inside it. The same method will help with other area word problems they see in 11+ practice. More questions like this are ready to try, perfect for building confidence with maths.com uk style problems.
