Primary 6 · Measurement & Geometry

P6 circles

In P6, your child finds the circumference and area of a circle, then of half and quarter circles, then of figures built from them. Halving works for the area. The perimeter needs the straight edge too.

Taught in: Term 2
Syllabus: 3 skills
Usual slip: Leaving out the diameter

Updated 12 October 2026

A circle with centre O and its radius marked as 10 cm

What your child learns in P6 circles

Three skills, each with what it looks like on a worksheet.

Follows the latest (2026) MOE syllabus

See the syllabus wording

area and circumference of circle
finding the area and perimeter of semicircle, quarter circle
finding the area and perimeter of composite figures made up of square, rectangle, triangle, semicircle and quarter circle

Circumference and area of a circle

The diameter is 2 radii. Circumference = π × diameter. Area = π × radius × radius. With radius 10 cm and π = 3.14, the circumference is 62.8 cm and the area is 314 cm².

Radius

Diameter

Half and quarter circles

For the area, take half or a quarter of the whole circle: 314 ÷ 2 = 157 cm². The perimeter is the curved arc plus the straight edges: 31.4 + 20 = 51.4 cm, not 62.8 ÷ 2.

Area: half the circle

Perimeter: arc + diameter

Figures made of several shapes

Split the figure into shapes your child knows. Add the areas: 600 + 157 = 757 cm². For the perimeter, trace only the outside. The dashed edge where the shapes join is inside, so it is left out.

A rectangle and a semicircle

Key facts and formulas

Term 2

\frac{22}{7}

Diameter and radius $d = 2r$
Circumference: the distance around $C = \pi d = 2\pi r$ Example $2 \times \pi \times 7 =$ $44\,\text{cm}$
Area of a circle $A = \pi r^{2}$ Example $\pi \times 7 \times 7 =$ $154\,\text{cm}^{2}$
Half circle: perimeter $\tfrac{1}{2}\pi d + d$ Example $\frac{1}{2} \times \pi \times 14 + 14 =$ $36\,\text{cm}$
Quarter circle: perimeter $\tfrac{1}{2}\pi r + 2r$ Example $\frac{1}{2} \times \pi \times 7 + 2 \times 7 =$ $25\,\text{cm}$
Half or quarter circle: area $\tfrac{1}{2}\pi r^{2} \text{ or } \tfrac{1}{4}\pi r^{2}$ Example $\frac{1}{4} \times \pi \times 14^{2} =$ $154\,\text{cm}^{2}$
Composite figuresArea: add or take away. Perimeter: the outside edge only.square − quarter circle → $14 \times 14 - 154 =$ $42\,\text{cm}^{2}$

Words to know

Radius: The distance from the centre of a circle to its edge.
Diameter: A straight line across the circle through the centre. It is 2 radii.
Circumference: The distance all the way round a circle.
Arc: The curved part of a half or quarter circle.
Perimeter: The distance round the whole outside edge, curved and straight parts together.

The sentence that costs the mark

A semicircle has a diameter of 14 cm. Find its perimeter. (Take $\pi = \frac{22}{7}$ )

What the working usually does

perimeter =half the circle=22 cm

Half of the circle's distance round is 22 cm. That is right for the curved part, and the working stops there.

What the question asked

perimeter =arc + diameter=36 cm

The perimeter is the whole edge. The arc is 22 cm, and the straight cut is the 14 cm diameter.

Halving the whole circle is the right move for the area of a semicircle, so it feels right for the perimeter too. But cutting a circle makes a straight edge the whole circle never had, and the half circumference never counted it.

The same P6 circles question, worked properly

Lah works through it the way she does every question in StudyLah: one step at a time, marking the picture as she goes.

The figure shows a quarter circle of radius 28 cm. Find its perimeter. (Take $\pi = \frac{22}{7}$ )

Step 1 of 5▌

The quarter circle has three edges, one curved arc and two straight radii. The perimeter goes all the way round.
The arc is a quarter of the circumference: $\frac{1}{4}$ × 2 × $\frac{22}{7}$ × 28 = 44 cm.
Stopping at 44 cm leaves out the two straight edges. Each one is a radius, so they add up to 28 + 28 = 56 cm.
Add the curved part and the straight parts: 44 + 56 = 100 cm.
So the perimeter of the quarter circle is 100 cm.

Every question in StudyLah comes with a walkthrough like this one.

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Two quick P6 circles questions

Try them together, then tap to check.

Question 1

A 3.2-m wire is cut into identical quarter circles of diameter 7 cm. What is the greatest number of quarter circles that can be formed? (Take $\pi = \frac{22}{7}$ )

Show answer

Answer25. One quarter circle uses its 5.5 cm arc plus two radii, 7 cm together, so 12.5 cm. The wire is 320 cm, and 320 ÷ 12.5 = 25.6.

Question 2

Rectangle PQRS sits in a quarter circle. PR = 14 cm and the shaded triangle PSR is 44 cm². Find the area of the unshaded parts. (Take $\pi = \frac{22}{7}$ )

Show answer

Answer110 cm². PR runs from the centre to the arc, so it is a radius. The quarter circle is 154 cm², and 154 − 44 = 110.

Helping at home

How to tell it has clicked

When a half or quarter circle asks for the perimeter, ask one thing before your child starts: which edges do we add? The answer you want names two kinds, the curved arc and the straight edges.

Ask for the radius of a circle 18 cm across. If the answer is 18, radius and diameter are still mixed up.

Try this tonight

Cut a roti prata in half. Ask how many kinds of edge one half has now. Two: the curved one, and the flat cut.

Then run a finger all the way round one half, back to the start. That is the perimeter, and the finger does not lift off at the end of the curve.

Before and after P6 circles

Builds on
Primary 4 Area and Perimeter
Splits for area, traces for perimeter
You are here
Primary 6 Circles
Finds the area and perimeter of circles

In the PSLE's hardest questions

More in Primary 6

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

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