11+ Maths: Word Problems with Compound Shapes (CEM & GL)
21 October 2026
Understanding compound shapes
Compound shapes are made by joining two or more simple shapes, such as rectangles, triangles or circles. In the 11+ CEM and GL exams, word problems often ask children to find the area or perimeter of these shapes. The challenge is to break the shape into manageable parts and solve each step carefully.
What to expect in word problems
Questions may describe a real-life scenario, like a garden with a patio, or a playground with a semi-circular end. Children need to identify which shapes are involved, what measurements are given, and which formulas to use for each part.
Key insight: Encourage your child to sketch the compound shape if no diagram is provided. Labelling all given measurements makes it much easier to spot which areas or perimeters to calculate.
Step-by-step example
A compound shape is made from a rectangle (5 cm by 4 cm) with a half-circle attached to one short side. The half-circle has a radius of 2 cm.
Step 1: Find the area of the rectangle.
Area = length × width = 5 × 4 = 20 cm².
Step 2: Find the area of the half-circle.
Area of a full circle = π × radius² = 3.14 × 2² = 3.14 × 4 = 12.56 cm².
Area of half-circle = 12.56 ÷ 2 = 6.28 cm².
Step 3: Add the areas together.
Total area = 20 + 6.28 = 26.28 cm².
The total area of the compound shape is 26.28 cm².
Supporting your child at home
Practise breaking down each word problem into smaller steps. Remind your child to check which measurements to use and whether to add or subtract areas, especially if a section is cut out. Encourage careful working and checking at each stage.
Building confidence for CEM and GL
Both exam boards use compound shapes to test understanding of area, perimeter, and problem-solving. Regular practice with a variety of shapes and contexts helps children feel prepared and able to tackle these questions in the real exam.
