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PSLE 2023 · Paper 2 · Q12 Measurement & Geometry · Area & perimeter 4 marks: 2 + 2 · long answer (2 parts) difficulty 4 of 5

PSLE 2023 Paper 2, Question 12: Area & perimeter

The answer

(a) \(132\) cm · (b) \(546\) cm²

PSLE 2023 Paper 2 Question 12 · Verified worked solution by the Genius Plus Academy teaching team

What this question tests

This is Question 12 of the PSLE 2023 Paper 2 Mathematics paper. It tests area & perimeter, in the Measurement & Geometry strand. It is worth 4 marks: 2 + 2. Open your copy of the paper at this question, then follow our full worked solution below.

Watch the walkthrough

Video: a Genius Plus Academy teacher solving PSLE 2023 Paper 2 Question 12

Teacher video · 2023 P2 Q12

Step-by-step solution

(a) The boundary of the shaded part is made up of circle arcs that together form exactly 3 full circles: \(3 \times \frac{22}{7} \times 14 = 3 \times 44 = 132\) cm.

Shaded circles whose arcs form three full circles — Marked-up figure from the GPA worked solution for (a), the boundary arcs are traced as 3 full circles of diameter 14 cm.

(b) By cut-and-paste, the shaded area equals the dashed rectangle through the corner centres plus the parts of the shaded circles outside it: the parts outside (\(\frac{3}{4} + \frac{3}{4} + \frac{1}{2}\) of a circle) minus the unshaded circle parts inside (\(\frac{1}{4} + \frac{1}{4} + \frac{1}{2}\)) come to exactly 1 full circle. Area \(= (14 \times 14) \times 2 + \frac{22}{7} \times 7 \times 7 = 392 + 154 = 546\) cm².

Cut-and-paste rearrangement for the shaded area — Cut-and-paste figure from the GPA worked solution for (b), the shaded parts rearranged into two \(14 \times 14\) squares plus one full circle.

Answer: (a) \(132\) cm · (b) \(546\) cm²

Same structure, different costume

A question is hard because of its structure, not its story.

Change egg tarts to badges, a tank to two tanks, a ring of card to a folded sheet, and a child sees a brand new problem. The lock underneath is the same, and so is the key. Once a student can name the structure, a whole row of questions that look different start to open the same way.

It is also where marks really leak. Across fourteen years of papers, the marks lost in PSLE math leak at the reading far more than at the arithmetic, which is exactly why recognising the structure fixes them. We call this Lock and Key: name the lock, then the key follows.

See what the paper rewards → The hardest questions, shown working →

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