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PSLE 2022 · Paper 2 · Q8 Measurement & Geometry · Area & perimeter 4 marks: 2 + 2 · long answer (2 parts) difficulty 4 of 5

PSLE 2022 Paper 2, Question 8: Area & perimeter

The answer

(a) \(138\) cm · (b) \(630\ \text{cm}^2\)

PSLE 2022 Paper 2 Question 8 · Verified worked solution by the Genius Plus Academy teaching team

What this question tests

This is Question 8 of the PSLE 2022 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 2022 Paper 2 Question 8

Teacher video · 2022 P2 Q8

Step-by-step solution

(a) Arc of the \(\frac{3}{4}\) circle (r = 14): \(\frac{3}{4} \times 2 \times \frac{22}{7} \times 14 = 66\) cm. Arc of the large quarter circle (r = 28): \(\frac{1}{4} \times 2 \times \frac{22}{7} \times 28 = 44\) cm. Plus the two straight lines: \(14 + 14\). Perimeter \(= 66 + 44 + 14 + 14 = 138\) cm.

Annotated figure from the GPA worked solution for (a): the perimeter pieces are colour-coded and the large quadrant's radius is found as 42 - 14 = 28 cm.

(b) Area of \(\frac{3}{4}\) circle: \(\frac{3}{4} \times \frac{22}{7} \times 14 \times 14 = 462\ \text{cm}^2\). The region between the 28 cm × 28 cm quarter-square and the large quadrant: \(28 \times 28 - \frac{1}{4} \times \frac{22}{7} \times 28 \times 28 = 784 - 616 = 168\ \text{cm}^2\). Shaded area \(= 462 + 168 = 630\ \text{cm}^2\).

The shaded region split into parts A and B with the area working — Figure from the GPA worked solution for (b): the shaded region is split into A (the ¾ circle) and B (square minus quadrant).

Answer: (a) \(138\) cm · (b) \(630\ \text{cm}^2\)

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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