Word Problems with Compound Shapes for 11+ Maths
21 October 2026
Why compound shapes matter
Compound shapes are a regular feature in 11+ maths word problems, especially for CEM and GL style exams. These questions test more than just area and perimeter. They check if your child can break down a complex picture and stay organised under pressure.
What is a compound shape
A compound shape is made by joining two or more simple shapes, usually rectangles or triangles. In 11+ exams, these often appear as L-shapes, T-shapes or shapes with a corner cut out. Some side lengths may be missing, so part of the challenge is working these out before calculating area or perimeter.
Practical tips for parents
Encourage your child to mark all known side lengths on the diagram first. Next, help them split the shape into parts they recognise, such as rectangles and triangles. Remind them to work out any missing lengths by using the information given. Tackle each section one at a time, then add up the results carefully.
Worked example
A compound shape is made from a rectangle and a triangle. The rectangle is 5 cm long and 4 cm wide. The triangle is attached to one side, with a base of 5 cm and a height of 3 cm.
Step 1: Area of rectangle 5 × 4 = 20 cm²
Step 2: Area of triangle (5 × 3) ÷ 2 = 7.5 cm²
Step 3: Add the two areas 20 + 7.5 = 27.5 cm²
The total area is 27.5 cm².
Avoiding common mistakes
Many children mix up area and perimeter or forget to find missing sides. Remind your child to label diagrams and double-check each step. Take it slow and encourage them to re-read the question before writing the final answer.
Key insight: Breaking a compound shape into simple parts and working through each section step by step is the most reliable way to solve these word problems.
