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PSLE 2019 · Paper 2 · Q16 Measurement & Geometry · Area & perimeter 5 marks: 2 + 3 difficulty 5 of 5

PSLE 2019 Paper 2, Question 16: Area & perimeter

The answer

(a) \(36\) cm (b) \(366.74\) cm

PSLE 2019 Paper 2 Question 16 · Verified worked solution by the Genius Plus Academy teaching team

What this question tests

This is Question 16 of the PSLE 2019 Paper 2 Mathematics paper. It tests area & perimeter, in the Measurement & Geometry strand. It is worth 5 marks: 2 + 3. Open your copy of the paper at this question, then follow our full worked solution below.

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Video: a Genius Plus Academy teacher solving PSLE 2019 Paper 2 Question 16

Teacher video · 2019 P2 Q16

Step-by-step solution

Semicircle figure with the three diameters tabulated (22 + a, b + 12 + a, b + b + 16) and the arcs and baseline segments highlighted — Annotated figure from the GPA worked solution: diameter equations tabulated (b = 10 cm, d = 36 cm); arcs and the five baseline segments highlighted for the perimeter.

(a) Let the diameter be \(d\). The 2nd upper semicircle overlaps each lower semicircle by \(22 - 12 = 10\) cm (the lower semicircle's diameter ends 22 cm from the figure's end and the gap between upper semicircles is 12 cm). So \(d = 10 + 16 + 10 = 36\) cm. (b) Boundary \(= 5\) semicircular arcs \(+\) the 5 solid baseline segments: \(2.5 \times \pi \times 36 + (22 + 12 + 16 + 12 + 22) = 90\pi + 84 = 366.7433... \approx 366.74\) cm.

Answer: (a) \(36\) cm (b) \(366.74\) cm

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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