Word Problems with Compound Shapes for 11+ Maths (CEM & GL)
21 October 2026
Understanding compound shapes
Compound shapes are made by joining two or more simple shapes, such as rectangles, squares or triangles. In the 11+ exam, children are often asked to solve word problems that involve finding the area or perimeter of these combined shapes.
How to approach word problems
Start by reading the problem carefully. Identify which simple shapes make up the compound shape. Sketching the shape and labelling all measurements can help your child see what is being asked.
Key insight: Breaking compound shapes into simple parts makes word problems clear and manageable
Worked example
A garden is made from a rectangle joined to a square. The rectangle is 8 cm long and 4 cm wide. The square has sides of 4 cm. What is the total area of the garden?
Step 1: Find the area of the rectangle
Area = length × width = 8 cm × 4 cm = 32 cm²
Step 2: Find the area of the square
Area = side × side = 4 cm × 4 cm = 16 cm²
Step 3: Add the two areas together
Total area = 32 cm² + 16 cm² = 48 cm²
The total area of the garden is 48 cm².
Practical tips for parents
Encourage your child to look for ways to split compound shapes into familiar parts. Remind them to check if any sides are shared or missing measurements. Practise drawing and labelling shapes to build confidence.
