Area of composite figures

Shapes made of shapes

A composite figure is made of simpler shapes: rectangles, triangles, circles. Floor plans, gardens, logos and L-shaped rooms are all composite figures.

Strategy 1: Add the parts

Decompose the figure into simple shapes, find each area, and add.

Example: An L-shaped room. Split it into two rectangles:

Strategy 2: Subtract the hole

Find the area of a big shape, then subtract the part that’s missing.

Example: A 10 m × 6 m lawn with a circular pond of radius 1.5 m.

• Lawn rectangle: 60 m²
• Pond: π × 1.5² ≈ 7.07 m²
• Grass: 60 − 7.07 ≈ 52.9 m²

Finding missing lengths

Often a side isn’t labelled. Use the sides you know.

Example: An L-shape is 12 cm wide at the bottom and 9 cm tall on the left. The top part is 5 cm wide, and the right side of the bottom part is 4 cm tall.

• Missing length across the step: 12 − 5 = 7 cm
• Missing height on the top part: 9 − 4 = 5 cm
• Split into: bottom 12 × 4 = 48 cm²; top 5 × 5 = 25 cm²
• Total: 73 cm²

Check with subtraction: whole rectangle 12 × 9 = 108; cut-out 7 × 5 = 35; 108 − 35 = 73 ✓.

Shapes with curves

Example: A window is a rectangle 80 cm wide and 100 cm tall, with a semicircle on top (diameter 80 cm).

• Rectangle: 8,000 cm²
• Semicircle: ½ × π × 40² ≈ 2,513 cm²
• Total ≈ 10,513 cm²

Shapes with triangles

Example: A house shape: a 6 m × 4 m rectangle with a triangle roof of base 6 m and height 2 m.

• 24 + ½ × 6 × 2 = 24 + 6 = 30 m²

Tips

1. Sketch and label the parts.
2. Write each area calculation separately.
3. Check that no part is counted twice or left out.
4. Keep all units the same and answer in square units.

Worked examples

Example 1: A T-shape: top bar 10 × 2, stem 2 × 6. Area?

20 + 12 = 32 square units.

Example 2: A 20 cm square with a 5 cm square cut from each corner. Area?

400 − 4 × 25 = 300 cm².

Example 3: A running track: a rectangle 100 m × 60 m with semicircles (diameter 60 m) on both ends. Area?

6,000 + π × 30² ≈ 6,000 + 2,827 = 8,827 m².

Common mistakes

• Overlapping parts, counting some area twice.
• Using the wrong missing length.
• Forgetting to halve for semicircles and triangles.

Try it yourself

1. An L-shape made of a 6 × 2 and a 3 × 4 rectangle (no overlap). Area?
2. A 12 m × 8 m yard has a 3 m × 2 m shed. Area of the rest?
3. A rectangle 10 cm × 4 cm with a semicircle (diameter 4 cm) on one short end. Area?

Answers: 1) 24 square units 2) 90 m² 3) 40 + 2π ≈ 46.3 cm²

Quick recap

• Decompose a composite figure into simple shapes and add.
• Or subtract missing parts from a bigger shape.
• Work out every missing length carefully.