PSLE Area and Perimeter Questions, Shown Working

Q: Are these solutions reliable?

Every solution was worked independently then checked against the verified GPA key: the official marking scheme where one exists, and a handwritten key for 2021. All three agreed on every answer. Mrs Eileen Toh signs off the mathematics.

PSLE area and perimeter questions, shown working.

The short version

Almost every hard area-and-perimeter question is cracked by three habits: split a figure into pieces you can measure, conserve the area while rebuilding the boundary when shapes are cut and rearranged, and drop the internal edges where pieces are joined. Get those three reflexes, and the rings, folds and composite figures stop being a surprise.

Based on GPA's tagged index of 709 PSLE questions, with frequency figures from the 664 questions in the 14 papers actually sat 2012 to 2025 and the MOE Specimen reported separately · every solution worked independently then checked against the verified GPA key · Mrs Eileen Toh signs off the mathematics · last reviewed 22 Jun 2026

In every PSLE Paper 2 for fourteen years running. Fourteen of fourteen.

Area and Perimeter is one of three structures that has appeared in every PSLE Paper 2 from 2012 to 2025, with no exceptions in the papers counted. Across the decade it is one of the most-tested structures we track, and it is also where some of the hardest questions in the paper live.

14 of 14

PSLE Paper 2 papers from 2012 to 2025 that featured an area-and-perimeter question, with no exceptions in the papers counted.

Area-and-perimeter questions across the decade, one of the most-tested structures in GPA's tagged index.

Habits that crack almost all of them: split the figure, conserve area and rebuild the boundary, drop the internal edges.

Frequency figures use the 664 questions from the 14 papers actually sat, with the MOE Specimen reported separately. This is honest analysis of past papers, not a forecast of the next one. Source: GPA tagged index.

2021 · Paper 2 · Q16 rearrangement

The ring cut into quarters and rearranged

Where to find it

This is a worded PSLE question, so we don’t reproduce it here. Find it in your Ten-Year Series (TYS) or the official paper — 2021 Paper 2, Q16, parts (a) and (b) (the area question where a ring is cut up and rearranged) — then follow our worked solution below.

Video: a Genius Plus Academy teacher solving PSLE 2021 Paper 2 Question 16

Teacher video · 2021 P2 Q16

The lock

Rearranging the pieces alarms children into recomputing everything. Two quiet truths survive the cut: the area does not change, and the new boundary is still made only of the original arcs and the two fresh straight cuts.

The key

Extract the ring width from the 42 cm span, then conserve area and rebuild the boundary.

Worked steps

The 42 cm width is 4 small-circle radii plus 2 ring-widths: \(42 = 4 \times 8 + 2w\), so \(2w = 10\) and \(w = 5\) cm.
Large radius \(= 8 + 5 = 13\) cm.
(a) Area is unchanged by rearranging: \(\pi(13^2) - \pi(8^2) = 3.14 \times (169 - 64) = 3.14 \times 105 = 329.7\) cm².
(b) The boundary is one whole outer circle, one whole inner circle, and two exposed 5 cm cuts: \(2 \times 3.14 \times 13 + 2 \times 3.14 \times 8 + 5 + 5 = 141.88\) cm.

Answer: (a) 329.7 cm². (b) 141.88 cm.

What makes it click. Rearranging is a magician's misdirection. Hold onto the two facts that survive the cut, area is conserved and the arcs still add to two full circles, and the shape's new look stops mattering.

Independently solved, matches the GPA handwritten key (2021 had a handwritten key, not a published marking scheme). Open the full worked solution →

2024 · Paper 2 · Q17 fold then cut

The paper that is folded, then cut

Where to find it

This is a worded PSLE question, so we don’t reproduce it here. Find it in your Ten-Year Series (TYS) or the official paper — 2024 Paper 2, Q17, parts (a) and (b) (the folding-and-cutting area and perimeter question) — then follow our worked solution below.

Video: a Genius Plus Academy teacher solving PSLE 2024 Paper 2 Question 17

Teacher video · 2024 P2 Q17

The lock

Folding makes two edges equal, and cutting reveals new edges. A child who treats the fold and the cut as unrelated cannot connect the 60 cm to anything. Let BC be one unit, write each perimeter in units, and use the difference.

The key

One unit on the unknown side, build both perimeters, solve.

Worked steps

Let BC \(=\) 1u, so BD \(=\) 4u. The flap X is a right triangle with legs 50 cm and 1u; Y is the remaining piece, whose outline runs along 3u, then 50, then 4u.
P(Y) minus P(X) \(= (3\text{u} + 50 + 4\text{u}) - (50 + 1\text{u}) = 6\text{u} = 60\) cm, so u \(= 10\) cm.
(a) BD \(= 4\text{u} = 40\) cm.
(b) Area of X \(= \frac{1}{2} \times 50 \times 10 = 250\) cm². The whole rectangle is \(50 \times 40 = 2000\) cm², and the fold removes two copies of X, so area of Y \(= 2000 - 2 \times 250 = 1500\) cm².

Answer: (a) BD = 40 cm. (b) 1500 cm².

What makes it click. The 60 cm is not a length you measure; it is a difference of perimeters, and once both perimeters are written in units of BC, that single sentence hands you the unit.

Independently solved, matches the GPA marking-scheme key. Open the full worked solution →

2023 · Paper 1 · Q15 the rare hard one in Paper 1

The rare hard one in Paper 1

Where to find it

This is a worded PSLE question, so we don’t reproduce it here. Find it in your Ten-Year Series (TYS) or the official paper — 2023 Paper 1, Q15 (the shaded-region fraction question) — then follow our worked solution below.

The lock

This sits in Paper 1, where the average question is gentle, so it is easy to rush. The 1 : 8 ratio fixes how high up the crossing point G sits, and from there the unshaded triangle is a single area calculation.

The key

Let the side be 3 units, use the ratio to find G's height, then subtract the one unshaded triangle.

Worked steps

Let AD \(=\) 3 units (so AE = EF = FD = 1) and let the rectangle's height be \(h\).
The ratio area EGF : area ABF \(=\) 1 : 8 places G at height \(h/4\) above AD (check: \(\frac{1}{2} \times 1 \times \frac{h}{4} : \frac{1}{2} \times 2 \times h = \frac{h}{8} : h = 1 : 8\)).
The only unshaded part is triangle BGC, with base 3 and height \(\frac{3h}{4}\): area \(= \frac{1}{2} \times 3 \times \frac{3h}{4} = \frac{9h}{8}\).
Rectangle area \(= 3h\), so shaded fraction \(= \frac{3h - \frac{9h}{8}}{3h} = \frac{\frac{15h}{8}}{3h} = \frac{5}{8}\).

Answer: shaded fraction = 5/8.

What makes it click. The small ratio is not decoration, it is the lever that fixes G's height, and once G is placed, a single triangle's area finishes the job. A reminder that Paper 1 can bite.

Independently solved, matches the GPA marking-scheme key. Open the full worked solution →

The overlap you forgot, the edge you could not see.

In a composite figure, the same two slips appear again and again. A child double-counts a shared region, so the area comes out too big, or counts an internal join-edge as part of the outside, so the perimeter comes out too long. Both are the cost of adding before looking.

The fix is a single habit, done before any arithmetic: mark every internal edge and every overlap on the figure first. Once the seams and the shared regions are visibly flagged, the area stops being double-counted and the perimeter stops borrowing edges it should never have touched.

For area

Mark every overlap. A region counted in two pieces must be subtracted once, or it is added twice.

For perimeter

Mark every internal edge. Seams where pieces meet are inside the figure, so they never belong to the outside boundary.

Questions parents ask

How often does area and perimeter appear in the PSLE?

It is one of three structures that has appeared in every PSLE Paper 2 from 2012 to 2025, fourteen of fourteen, with no exceptions in the papers counted. Across the decade it is one of the most-tested structures we track, 61 questions in GPA's tagged index. This is honest analysis of past papers, not a forecast of the next one.

What makes these questions hard, and how do you crack them?

They are hard because of structure, not arithmetic. Three habits crack almost all of them: split a figure into pieces you can measure, conserve the area while rebuilding the boundary when shapes are cut and rearranged, and remember that internal join-edges are never part of the outside perimeter.

What is the most common mistake children make?

Forgetting the overlap or the hidden internal edge in a composite figure. A child double-counts a shared region, so the area is too big, or counts an internal join-edge as part of the outside, so the perimeter is too long. The fix is to mark every internal edge and every overlap before adding anything.

Are these solutions reliable?

Every solution here was worked independently and then checked against the verified GPA key: the official marking scheme where one exists, and a handwritten key for 2021. All three agreed on every answer. Mrs Eileen Toh signs off the mathematics. Browse the full set in our worked-solutions library.

PSLE area and perimeter questions, shown working.

In every PSLE Paper 2 for fourteen years running. Fourteen of fourteen.

Three habits crack area and perimeter.

Part-whole on a figure

Conserve area, rebuild the boundary

Internal edges are not perimeter

The ring cut into quarters and rearranged

The paper that is folded, then cut

The rare hard one in Paper 1

The overlap you forgot, the edge you could not see.

The 10 PSLE Question Types, cheat sheet

This page trains one reflex. The Intensive trains all ten.

Keep reading

Questions parents ask

See how your child reads a figure.