Composite Area

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Strategy for Composite Areas

Composite (compound) shapes are made of two or more simple shapes joined together — or a simple shape with a piece cut out. There are two key approaches:

Method 1: ADD

Split the shape into simpler parts.
Find each area separately.
Add them together.

A = A₁ + A₂

Method 2: SUBTRACT

Find the area of a large simple shape.
Subtract the cut-out piece.
Result = remaining area.

A = A_big − A_cut

💡 Tip: Both methods work for L-shapes. Choose whichever feels easier. Always label the parts clearly and show your working.

✓ Quick Check 1 — Strategy for Composite Areas

Question 1 of 10

L-Shape Decomposition

An L-shape that is 10 cm wide and 8 cm tall, with a 4 cm × 3 cm notch cut from the top-right corner.

📄 Worked: L-shape (subtract method)

Step 1 — Big rectangle

10 × 8 = 80 cm²

Step 2 — Notch cut out

4 × 3 = 12 cm²

Step 3 — Subtract

80 − 12 = 68 cm²

T-Shape

A T-shape split into a horizontal top bar and a vertical stem. The two colours show the two rectangles.

📄 Worked: T-shape

Step 1 — Top bar

12 × 2 = 24 cm²

Step 2 — Vertical stem

4 × 8 = 32 cm²

Step 3 — Total

24 + 32 = 56 cm²

✓ Quick Check 2 — L-Shapes and Rectilinear Shapes

Question 1 of 10

Rectangle with a Semicircle

A rectangle (10 cm × 6 cm) with a semicircle of diameter 6 cm attached to one end (radius = 3 cm).

📄 Worked: Rectangle + Semicircle

Step 1 — Rectangle

A = 10 × 6 = 60 cm²

Step 2 — Semicircle (radius = 3 cm)

A = π × r² ÷ 2 = π × 9 ÷ 2 = 14.14 cm²

Step 3 — Total

60 + 14.14 = 74.14 cm²

Note

This uses full-precision π. If a question tells you to use π ≈ 3.14 instead, you'll get 74.13 cm² — a 0.01 cm² difference from rounding, not a mistake.

💡 Semicircle formula: A = ½ × π × r². Always halve the full circle area. Make sure you use the radius, not the diameter.

✓ Quick Check 3 — Rectangle + Semicircle Composites

Question 1 of 10

Annulus (Ring Shape)

An annulus is a large circle with a smaller circle removed from the centre — like a ring or a washer. Subtract the inner circle area from the outer circle area.

📄 Worked: Annulus (R = 8 cm, r = 3 cm)

Step 1 — Outer circle

A = π × 8² = π × 64 = 201.06 cm²

Step 2 — Inner circle (hole)

A = π × 3² = π × 9 = 28.27 cm²

Step 3 — Subtract

201.06 − 28.27 = 172.79 cm²

Annulus area = π × R² − π × r² = π(R² − r²)

✓ Quick Check 4 — Shapes with Semicircles and Cut-Outs

Question 1 of 10

✓ Quick Check 5 — Multi-Step Real Life Problems

Question 1 of 10

Practice: Extra Questions

Work out each answer, then type it in and click Check to see if you're right.

#	Question	Your answer	Result
1	An L-shape is made from a 8 cm × 6 cm rectangle with a 3 cm × 2 cm rectangle removed from one corner. What is the area?
2	A shape is formed by joining a 10 cm × 4 cm rectangle and a 5 cm × 3 cm rectangle. What is the total area?
3	A 12 cm × 8 cm rectangle has a 4 cm × 4 cm square cut from one corner. What is the remaining area?
4	A T-shape: a 10 cm × 2 cm strip sits on top of a 6 cm × 4 cm rectangle. What is the total area?
5	Two rectangles: 7 cm × 5 cm and 3 cm × 5 cm placed side by side. What is the total area?
6	An L-shape: split into a 9 cm × 3 cm rectangle and a 4 cm × 6 cm rectangle. What is the total area?
7	L-shape: rectangle 8 cm × 3 cm plus rectangle 4 cm × 5 cm. What is the total area?
8	A 10 cm × 6 cm rectangle has a 3 cm × 2 cm piece cut from a corner. What is the remaining area?
9	A rectangle 6 cm × 4 cm has a triangle (base 6 cm, height 3 cm) sitting on top. What is the total area?
10	A rectangle 10 cm × 6 cm has a semicircle (r = 3 cm) attached to one side. Use π = 3.14. What is the total area to 2 d.p.?
11	A square 8 cm × 8 cm has a circle (r = 2 cm) cut from the middle. Use π = 3.14. What is the remaining area to 2 d.p.?

⚠ Things to Watch Out For

Make sure you split the composite shape into recognised sub-shapes correctly — an incorrect split leads to wrong areas.
If a sub-shape is cut out (subtracted), subtract its area — don't add it again by mistake.
Identify the correct dimensions for each sub-shape; some measurements may need to be calculated from the overall dimensions first.
Don't double-count a shared boundary — it is an edge of one shape only, not two.
Give your final area in square units throughout (cm², m², etc.).

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Learning Objectives

Real-World Applications

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Practice: Extra Questions

⚠ Things to Watch Out For