Year 10: Compound shapes and circles

Compound shape questions ask you to break a larger figure into simpler parts such as rectangles, triangles, and semicircles. In Year 10, these problems often combine area, perimeter, circumference, and practical contexts such as paving or tiling.

Split the shape into known pieces, calculate each part, then add or subtract carefully.

Area of a compound shape

The most reliable method is to redraw the shape as two or more simpler regions.

Example 1: A shape is made from a rectangle

8 m b y 5 m

with a right triangle on top of base

8 m

and height

3 m

. Find the total area.

Rectangle area $= 8 \times 5 = 40 m^{2}$ .
Triangle area $= 1 / 2 \times 8 \times 3 = 12 m^{2}$ .
Total area $= 40 + 12 = 52 m^{2}$ .

Circumference and curved boundaries

If a curved edge belongs to a circle, use circumference formulas. Full circumference is $2 π r$ or $π d$ . For semicircles or sectors, take the correct fraction.

Example 2: Find the circumference of a circle with radius

7 cm

Use $C = 2 π r$ .
$C = 2 \times π \times 7 = 14 π cm$ .
This is about $44.0 cm$ .

Practical tiling questions

Tiling problems usually compare the total area to the area of one tile. Divide at the end and round up if only whole tiles can be bought.

Example 3: A patio has area

18 m^{2}

. Tiles each cover

0.25 m^{2}

. How many tiles are needed?

$18 \div 0.25 = 72$ .
So $72$ tiles are needed.

Common mistakes

Adding a side into the perimeter when it is inside the shape, not on the outside boundary.
Using diameter where the formula needs radius.
Forgetting that a semicircle has half the curved circumference, not half the whole boundary plus the diameter unless asked for total perimeter.

Year 10: Compound shapes and circles

Area of a compound shape

Circumference and curved boundaries

Practical tiling questions

Common mistakes

Skills to practise