Split L-shapes and other compound shapes into rectangles and triangles to find their area and perimeter. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A compound shape is rectangles, triangles, trapezia or circles stuck together — or one of them with a bite taken out. Split it (dotted lines on the diagram help) and add the pieces, or surround it with a rectangle and subtract the missing corner. The perimeter is only the outer path; inner cuts that disappear do not count.
Circles in compound shapes: a semicircle sitting on a rectangle adds half the circumference (not including the diameter if that diameter is already an edge of the rectangle). Write each area on the split diagram so the marker can see the parts.
Split, or big-minus-bite. Label every length you use, including the ones you had to find by subtracting. Perimeter of an L cut from a rectangle’s corner equals the original rectangle’s perimeter.
Objectives
Draw a line that makes rectangles you know.
An L-shape can be a large rectangle minus a small rectangle.
The full width is the sum of the pieces along that side.
Key points
Split a compound shape into rectangles (and triangles) with a dotted line.
Work out missing side lengths by adding or subtracting the given ones.
Add the areas of the pieces, or subtract a cut-out from a big rectangle.
Find the perimeter by adding every outside edge once.
Worked examples
Example 1
A compound shape is a 5 cm by 3 cm rectangle joined to a 2 cm by 4 cm rectangle. What is the total area?
3 marks
First rectangle: 5 × 3 = 15 cm².
Second rectangle: 2 × 4 = 8 cm².
The areas are joined, so the total is 15 + 8 = 23 cm².
Answer: 23 cm²
Common slips
Slip: First rectangle: 5 + 3 = 8. Area is length × width, not length + width.
Slip: Second rectangle: 2 + 4 = 6. Area is length × width, not length + width.
Slip: The total is 8 + 6 = 14 cm². That adds lengths. The total has to be a sum of areas.
Example 2
A rectangle is 8 cm by 6 cm. A 4 cm by 2 cm rectangle is cut out of it. What is the area that is left?
3 marks
Whole rectangle: 8 × 6 = 48 cm².
Piece cut out: 4 × 2 = 8 cm².
The piece is removed, so the area left is 48 − 8 = 40 cm².
Answer: 40 cm²
Common slips
Slip: Whole rectangle: 8 + 6 = 14. Area is length × width, not length + width.
Slip: Piece cut out: 4 + 2 = 6. Area is length × width, not length + width.
Slip: The piece is part of the shape, so the area is 48 + 8 = 56 cm². A piece that is cut out has to be taken away, not added.
Example 3
A compound shape is a 5 cm by 4 cm rectangle joined to a 3 cm by 2 cm rectangle. What is the total area?
3 marks
First rectangle: 5 × 4 = 20 cm².
Second rectangle: 3 × 2 = 6 cm².
The areas are joined, so the total is 20 + 6 = 26 cm².
Answer: 26 cm²
Common slips
Slip: First rectangle: 5 + 4 = 9. Area is length × width, not length + width.
Slip: Second rectangle: 3 + 2 = 5. Area is length × width, not length + width.
Slip: The total is 9 + 5 = 14 cm². That adds lengths. The total has to be a sum of areas.
Questions and answers
GCSE Maths area of compound shapes questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A rectangle is 9 cm by 6 cm. A 3 cm by 2 cm rectangle is cut out of it. What is the area that is left?
Show answer
Answer: 48 cm²
Whole rectangle: 9 × 6 = 54 cm².
Piece cut out: 3 × 2 = 6 cm².
M1 — Whole rectangle: 9 × 6 = 54 cm².
A1 — Answer 48 cm²
Question 2 Easy2 marks
A compound shape is a 5 cm by 5 cm rectangle joined to a 4 cm by 3 cm rectangle. What is the total area?
Show answer
Answer: 37 cm²
First rectangle: 5 × 5 = 25 cm².
Second rectangle: 4 × 3 = 12 cm².
M1 — First rectangle: 5 × 5 = 25 cm².
A1 — Answer 37 cm²
Question 3 Medium2 marks
A rectangle is 11 cm by 6 cm. A 4 cm by 3 cm rectangle is cut out of it. What is the area that is left?
Show answer
Answer: 54 cm²
Whole rectangle: 11 × 6 = 66 cm².
Piece cut out: 4 × 3 = 12 cm².
M1 — Whole rectangle: 11 × 6 = 66 cm².
A1 — Answer 54 cm²
Question 4 Medium2 marks
A compound shape is a 5 cm by 7 cm rectangle joined to a 3 cm by 4 cm rectangle. What is the total area?
Show answer
Answer: 47 cm²
First rectangle: 5 × 7 = 35 cm².
Second rectangle: 3 × 4 = 12 cm².
M1 — First rectangle: 5 × 7 = 35 cm².
A1 — Answer 47 cm²
Question 5 Hard2 marks
A rectangle is 8 cm by 7 cm. A 3 cm by 2 cm rectangle is cut out of it. What is the area that is left?
Show answer
Answer: 50 cm²
Whole rectangle: 8 × 7 = 56 cm².
Piece cut out: 3 × 2 = 6 cm².
M1 — Whole rectangle: 8 × 7 = 56 cm².
A1 — Answer 50 cm²
Question 6 Hard2 marks
A compound shape is a 5 cm by 9 cm rectangle joined to a 3 cm by 2 cm rectangle. What is the total area?
Show answer
Answer: 51 cm²
First rectangle: 5 × 9 = 45 cm².
Second rectangle: 3 × 2 = 6 cm².
M1 — First rectangle: 5 × 9 = 45 cm².
A1 — Answer 51 cm²
Question 7 Exam-style3 marks
A rectangle is 10 cm by 7 cm. A 4 cm by 3 cm rectangle is cut out of it. What is the area that is left?
Show answer
Answer: 58 cm²
Whole rectangle: 10 × 7 = 70 cm².
Piece cut out: 4 × 3 = 12 cm².
The piece is removed, so the area left is 70 − 12 = 58 cm².
M1 — Whole rectangle: 10 × 7 = 70 cm².
M1 — Piece cut out: 4 × 3 = 12 cm².
A1 — Answer 58 cm²
Common mistakes
Most lost marks on this topic are one slip.
Multiplying the longest length by the tallest height of an L-shape.
That includes a rectangle that is not part of the shape, unless you subtract it.
Adding a length to an area.
Add areas to areas.
Using different units in one product.
Convert first.
Spot the slip
A compound area is usually found by
adding or subtracting simple areas
adding all the outside lengths
multiplying every number you can see
Show the slip
adding or subtracting simple areas Split the shape, then combine the areas.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write missing lengths on the diagram first — finding them is often a mark on its own.
Show each piece's area as a separate line, then the total; a slip in one piece still earns method marks.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.