Area and Perimeter • Topic 6 of 6

Composite Figures

A composite figure is built from simpler shapes joined together — for example a rectangle with a square or triangle attached, or a shape with a piece cut out. To find its area, break it into the basic shapes, find each area separately, and add them (or subtract a removed piece). A rectangle of area 50 with an added square of area 9 has total area 59. The skill is decomposing the figure correctly and keeping track of which parts add and which subtract. Perimeter of a composite figure is the total outer boundary, so include only the outside edges, not internal joins.

An L-shaped figure made of an 8 by 5 rectangle and a 3 by 3 squareComposite figure8 × 53 × 385Total area = 40 + 9 = 49

✅ Solved examples

1. A 5×4 rectangle has a 2×2 square attached. Find the total area.
20 + 4 = 24.
2. A 6×8 rectangle with a 3×3 square added. Total area?
48 + 9 = 57.
3. A 10×10 square has a 4×4 square removed. Find the remaining area.
100 − 16 = 84.
4. A 7×5 rectangle plus a triangle of area 6. Total area?
35 + 6 = 41.

✏️ Practice — try these, take hints as needed

1. A 6×5 rectangle has a 2×2 square attached. Total area?
Add the two areas.
30 + 4.
—
34.
2. A 9×4 rectangle with a 3×3 square added. Total area?
36 + 9.
—
—
45.
3. An 8×8 square has a 2×2 square removed. Remaining area?
Subtract.
64 − 4.
—
60.
4. A 10×6 rectangle plus a triangle of area 12. Total area?
60 + 12.
—
—
72.
5. A 12×5 rectangle with a 5×5 square attached. Total area?
60 + 25.
—
—
85.

📝 Topic test — 8 questions

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