What is the diameter of the largest circle inside a square?

It equals the side of the square; inside a rectangle it equals the shorter side.

Why does a semicircle perimeter include the diameter?

The perimeter is the whole boundary, which for a semicircle is the arc plus one diameter.

How do I find the area of a ring?

Subtract the inner circle from the outer one, that is 3.14 × (R × R − r × r).

P6 Maths Composite Shapes Paper 1: Basics

2026-11-09

Tutor Prep Guide · P6 Maths

Ten original items, each with an answer and a one-line explanation.

Direct answers　Items 1-3 are basic, 4-6 intermediate and 7-9 challenge, with item 10 as the error review. Time yourself first, then check every answer and redo the wrong ones.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	20
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: P6 Maths Composite Shapes with Circles
Level	P6

02　Questions (10 items)

FoundationA square has side 10 cm. The largest possible circle is drawn inside it. Find the area of the circle.
FoundationA rectangle is 12 cm long and 8 cm wide. What is the diameter of the largest circle that fits inside?
FoundationFind the area of a quarter circle of radius 6 cm.
IntermediateA square of side 10 cm has its largest inscribed circle cut out. Find the remaining area.
IntermediateA semicircle has diameter 10 cm. Find its perimeter, including the diameter.
IntermediateA rectangle 20 cm by 10 cm has a semicircle of radius 5 cm removed from each end. Find the remaining area.
ChallengeFind the perimeter of a quarter circle of radius 14 cm.
ChallengeA ring has outer radius 10 cm and inner radius 6 cm. Find its area.
ChallengeA semicircular garden has diameter 20 m. Turf costs 15 dollars per square metre. Find the total cost.
Error redoError review: a pupil gives 3.14 × 12 ÷ 2 = 18.84 cm as the perimeter of a semicircle of diameter 12 cm. What is the correct perimeter?

03　Answers and one-line notes

#	Answer	One-line note
1	78.5 cm²	The largest circle has diameter equal to the side, so the radius is 5 cm and 3.14 × 5 × 5 = 78.5 cm².
2	8 cm	The diameter is limited by the shorter side, so it is 8 cm.
3	28.26 cm²	3.14 × 6 × 6 ÷ 4 = 28.26 cm².
4	21.5 cm²	The square is 100 cm² and the circle is 78.5 cm², so 21.5 cm² remains.
5	25.7 cm	The arc is 3.14 × 10 ÷ 2 = 15.7 cm, and adding the 10 cm diameter gives 25.7 cm.
6	121.5 cm²	The two semicircles make one circle of 78.5 cm², so 200 − 78.5 = 121.5 cm² remains.
7	49.98 cm	The arc is 2 × 3.14 × 14 ÷ 4 = 21.98 cm, and two radii add 28 cm, giving 49.98 cm.
8	200.96 cm²	3.14 × (100 − 36) = 200.96 cm².
9	2355 dollars	The area is 3.14 × 100 ÷ 2 = 157 m², so 157 × 15 = 2355 dollars.
10	30.84 cm	The perimeter of a semicircle includes the diameter: 18.84 + 12 = 30.84 cm.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.