Free worked solutions for PSLE Mathematics, with a video for every Paper 2 question we have filmed · Browse the library →

PSLE 2023 · Paper 2 · Q17 Measurement & Geometry · Area & perimeter 4 marks: 2 + 2 · long answer (2 parts) difficulty 5 of 5

PSLE 2023 Paper 2, Question 17: Area & perimeter

The answer

(a) \(PQ = 21\) cm · (b) \(RS = 13\) cm

PSLE 2023 Paper 2 Question 17 · Verified worked solution by the Genius Plus Academy teaching team

What this question tests

This is Question 17 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 17

Teacher video · 2023 P2 Q17

Step-by-step solution

(a) Breaking Figure 2 into its 3 trapeziums shows that the three separate perimeters equal Figure 2's perimeter plus the 4 hidden \(PQ\) join-edges: \(3 \times 96 = 204 + 4 \times PQ \Rightarrow PQ = (288 - 204) \div 4 = 21\) cm.

Figure 2 broken into three trapeziums — Figure from the GPA worked solution for (a), Figure 2 separated into 3 trapeziums with the 4 hidden \(PQ\) join-edges marked.

(b) Two such trapeziums form a rectangle of width \(PQ = 21\) cm. Area of 2 trapeziums \(= 1932 \div 2 = 966\) cm², so the rectangle's length \(= 966 \div 21 = 46\) cm. From Figure 3, \(RS = 46 - 21 - 12 = 13\) cm.

Figure 3 with the two-trapezium rectangle — Figure from the GPA worked solution for (b), Figure 3 annotated, and two trapeziums forming a \(21 \times 46\) cm rectangle, giving \(RS = 13\) cm.

End of Paper 2 answers.

Answer: (a) \(PQ = 21\) cm · (b) \(RS = 13\) 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 →

Want more questions like this, with worked solutions?

We will send a set to practise. One email, no spam.