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.

Work through the sections in order, then try the linked Year 10 skill quizzes after each section.

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 $= 40 + 12 = 52 m^{2}$ .

Skill quiz: Split a shape into simpler regions

Identify the component rectangles, triangles or circular regions before adding or subtracting their areas.

Calculate the area of a compound shape

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 $44.0 cm$ .

Skill quizzes: Calculate curved boundary lengths

Start with Level 1 circumference questions, then progress to Level 2 and check radius versus diameter.

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.

Skill quiz: Calculate the number of tiles

Compare the total area with the area of one tile and round up when whole tiles are required.

Covering shapes with tilesPremium

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.

Skill quiz: Check area and outside boundaries

Practise compound planar shapes and distinguish interior edges from the outside perimeter.

Level 1: Calculate the properties of compound planar shapes