IGCSE Maths 0580 Area and Perimeter Past Paper Questions and Worked Solutions

By /
IGCSE Maths (0580) · Mensuration · 5.2

Every area and perimeter question from 10 Cambridge IGCSE Mathematics (0580) past papers (May/June 2025 to May/June 2026), syllabus section 5.2. 13 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/12/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Mensuration past paper questions.

0580 Area and Perimeter past paper questions: Core (Papers 1 and 3)

11 markCore

May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q4

The diagram shows a shape drawn on a 1 cm² grid. By counting squares, estimate the area of the shape.

0580/12 May/June 2026 Q4 – curved shape drawn on a 1 cm squared grid
Show solution
  1. Count the whole squares inside the shape first.
  2. Then look at the part squares. Pair them up so that two roughly-half squares count as one whole square.
  3. Add the two totals together.
  4. Estimate: about 12 cm²
Note: This is an estimate. Any answer from 11 cm² to 14 cm² is accepted.
Answer about 12 cm²
21 markCore

May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q8

A triangle has base 10 cm and perpendicular height 6 cm. Work out the area of the triangle.

0580/12 May/June 2026 Q8 – triangle with base 10 cm and height 6 cm6 cm10 cmNOT TOSCALE
Show solution
  1. Area of a triangle = 1⁄2 × base × height.
  2. Area = 1⁄2 × 10 × 6 = 1⁄2 × 60 = 30 cm²
Answer 30 cm²
32 marksCore

May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q13(b)

Trapezium T has parallel sides 2 cm and 4 cm and height 2 cm. On the grid, draw a rectangle with the same area as trapezium T.

Show solution
  1. Area of a trapezium = 1⁄2(a + b)h.
  2. Area of T = 1⁄2 × (2 + 4) × 2 = 1⁄2 × 6 × 2 = 6 cm².
  3. A rectangle with area 6 cm² needs length × width = 6.
  4. Draw, for example, a rectangle 3 cm by 2 cm (or 6 cm by 1 cm).
Answer 3 cm by 2 cm
41 markCore

May/June 2026 · Paper 3 · 0580/33/M/J/26 · Q3(b)

The diagram shows shapes drawn on a 1 cm² grid. Find the area of shape B.

0580/33 May/June 2026 Q3 – shaded shape and shapes A, B, C, D and E on a 1 cm squared grid
Show solution
  1. Each small square is 1 cm².
  2. Count the whole squares inside shape B, then pair up the half squares so that each pair makes one whole square.
  3. Area of B = 14 cm²
Answer 14 cm²
52 marksCore

May/June 2026 · Paper 3 · 0580/33/M/J/26 · Q7

Diagram A shows a square of side 15 cm cut into two pieces: a 5 cm strip and a 10 cm strip. The pieces are rearranged to form diagram B, a T-shape, with no overlaps. Find the perimeter of diagram B.

0580/33 May/June 2026 Q7 – diagram A, a 15 cm square cut into strips 5 cm and 10 cm wide, and diagram B, the strips arranged as a T-shape5 cm10 cmdiagram A10 cmdiagram BNOT TOSCALE
Show solution
  1. The two pieces are a 5 cm by 15 cm strip and a 10 cm by 15 cm strip.
  2. In diagram B the 5 cm strip lies across the top of the 10 cm strip. It is 15 cm long, so it sticks out (15 − 10) ÷ 2 = 2.5 cm on each side.
  3. Go round the outside: top 15, two ends 5 + 5, two overhangs 2.5 + 2.5, two long sides 15 + 15, bottom 10.
  4. 15 + 5 + 5 + 2.5 + 2.5 + 15 + 15 + 10 = 70 cm
  5. Check: The two strips have perimeters 40 cm and 50 cm. The 10 cm where they touch is hidden on both, so 90 − 10 − 10 = 70 ✓
Answer 70 cm
61 markCore

Feb/Mar 2026 · Paper 3 · 0580/32/F/M/26 · Q2

The diagram shows a shape drawn on a 1 cm² grid. By counting squares, estimate the area of the shape.

0580/32 February/March 2026 Q2 – curved shape on a 1 cm squared grid
Show solution
  1. Count the whole squares inside the shape first.
  2. Then look at the part squares. Pair them up so that two roughly-half squares count as one whole square.
  3. Add the totals together: about 20 cm²
Note: This is an estimate. Any answer from 19 cm² to 21 cm² is accepted.
Answer about 20 cm²
72 marksCore

Oct/Nov 2025 · Paper 1 · 0580/12/O/N/25 · Q17

A trapezium has parallel sides 8 cm and 14 cm and perpendicular height 6 cm. Calculate the area of this trapezium.

0580/12 October/November 2025 Q17 – trapezium with parallel sides 8 cm and 14 cm and height 6 cm8 cm14 cm6 cmNOT TOSCALE
Show solution
  1. Area of a trapezium = 1⁄2(a + b)h, where a and b are the parallel sides.
  2. Area = 1⁄2 × (8 + 14) × 6.
  3. = 1⁄2 × 22 × 6 = 11 × 6 = 66 cm²
Answer 66 cm²
86 marksCore

Oct/Nov 2025 · Paper 3 · 0580/31/O/N/25 · Q13

(a) The surface area of a solid cube is 121.5 cm². Calculate the length of the side of the cube.

(b) A trapezium has parallel sides 10 cm and 15 cm and height h cm. The area of the trapezium is 106.25 cm². (i) Calculate the height of the trapezium. (ii) Convert 106.25 cm² into m².

Show solution
Part (a)
  1. A cube has 6 identical square faces, so one face has area 121.5 ÷ 6 = 20.25 cm².
  2. The side length is the square root of the face area: √20.25 = 4.5 cm
Answer 4.5 cm
Part (b)(i)
  1. Area of a trapezium = 1⁄2(a + b)h.
  2. 1⁄2 × (10 + 15) × h = 106.25, so 12.5h = 106.25.
  3. h = 106.25 ÷ 12.5 = 8.5 cm
Answer 8.5 cm
Part (b)(ii)
  1. 1 m = 100 cm, so 1 m² = 100 × 100 = 10 000 cm².
  2. Divide by 10 000: 106.25 ÷ 10 000 = 0.010625 m²
Answer 0.010625 m²
92 marksCore

May/June 2025 · Paper 1 · 0580/13/M/J/25 · Q14

The diagram shows a trapezium with parallel sides 4 cm and 10 cm and height h cm. The area of the trapezium is 42 cm². Work out the value of h.

0580/13 May/June 2025 Q14 – right trapezium with parallel sides 4 cm and 10 cm and height h cm4 cm10 cmh cmNOT TOSCALE
Show solution
  1. Area of a trapezium = 1⁄2(a + b)h.
  2. Substitute: 1⁄2 × (4 + 10) × h = 42.
  3. Simplify: 1⁄2 × 14 = 7, so 7h = 42.
  4. Divide by 7: h = 6
Answer 6

0580 Area and Perimeter past paper questions: Extended (Papers 2 and 4)

102 marksExtended

May/June 2026 · Paper 2 · 0580/21/M/J/26 · Q4

A rectangle has width 6 cm. The width of the rectangle is 1⁄12 of the perimeter of the rectangle. Work out the length of the rectangle.

Show solution
  1. The width is 1⁄12 of the perimeter, so the perimeter is 12 times the width: 12 × 6 = 72 cm.
  2. Perimeter = 2 × length + 2 × width, so 2 × length = 72 − 2 × 6 = 60.
  3. Length = 60 ÷ 2 = 30 cm
Answer 30 cm
112 marksExtended

Oct/Nov 2025 · Paper 2 · 0580/21/O/N/25 · Q4

The area of a triangle is 12 cm². The length of the base of the triangle is 8 cm. Work out the height of the triangle.

Show solution
  1. Area of a triangle = 1⁄2 × base × height.
  2. Substitute: 1⁄2 × 8 × h = 12, so 4h = 12.
  3. h = 12 ÷ 4 = 3 cm
Answer 3 cm
122 marksExtended

Oct/Nov 2025 · Paper 2 · 0580/23/O/N/25 · Q4

A rectangle measures 5 cm by 19 cm. Two of these rectangles are joined to make a T-shape. Work out the perimeter of the shape.

0580/23 October/November 2025 Q4 – two 5 cm by 19 cm rectangles joined to make a T-shape19 cm5 cm5 cm19 cmNOT TOSCALE
Show solution
  1. Each rectangle has perimeter 2 × (5 + 19) = 48 cm, so two rectangles have 96 cm of edge altogether.
  2. Where the rectangles join, a 5 cm edge from each one is hidden inside the T-shape.
  3. Perimeter = 96 − 5 − 5 = 86 cm
Answer 86 cm
138 marksExtended

Oct/Nov 2025 · Paper 4 · 0580/42/O/N/25 · Q7

(a) A parallelogram has sides 6.51 m and x m. It has the same perimeter as a circle with radius 4 m. Show that x = 6.06 m, correct to 2 decimal places.

(b) The floor of a room is a parallelogram with sides 6.51 m and 6.06 m. The 6.06 m side makes an angle of 36° with the perpendicular height. It costs $18 per square metre to tile the floor. Calculate the total cost.

0580/42 October/November 2025 Q7 – parallelogram with sides 6.51 m and 6.06 m and a 36° angle to the height36°6.51 m6.06 mNOT TOSCALE
Show solution
Part (a)
  1. Perimeter of the circle (its circumference) = 2πr = 2 × π × 4 = 25.132… m.
  2. Perimeter of the parallelogram = 2 × 6.51 + 2x = 13.02 + 2x.
  3. Set them equal: 13.02 + 2x = 25.132…, so 2x = 12.112… and x = 6.056…
  4. To 2 decimal places: x = 6.06 m ✓
Answer x = 6.06 m
Part (b)
  1. The area of a parallelogram = base × perpendicular height. First find the height.
  2. The 6.06 m side is the hypotenuse, and the height is adjacent to the 36° angle, so use cos.
  3. Height = 6.06 × cos 36° = 4.902… m.
  4. Area = 6.51 × 4.902… = 31.91… m².
  5. Cost = 31.91… × 18 = 574.4…
  6. $574 (574 or 575 accepted)
Answer $574

Question papers used on this page

All area and perimeter questions above, listed by 0580 question paper code.

QP codeFile namePaperQuestions
0580/12/M/J/260580_s26_qp_12May/June 2026 · Paper 1 (Core)Q4, Q8, Q13(b)
0580/21/M/J/260580_s26_qp_21May/June 2026 · Paper 2 (Extended)Q4
0580/33/M/J/260580_s26_qp_33May/June 2026 · Paper 3 (Core)Q3(b), Q7
0580/32/F/M/260580_m26_qp_32Feb/Mar 2026 · Paper 3 (Core)Q2
0580/12/O/N/250580_w25_qp_12Oct/Nov 2025 · Paper 1 (Core)Q17
0580/21/O/N/250580_w25_qp_21Oct/Nov 2025 · Paper 2 (Extended)Q4
0580/23/O/N/250580_w25_qp_23Oct/Nov 2025 · Paper 2 (Extended)Q4
0580/31/O/N/250580_w25_qp_31Oct/Nov 2025 · Paper 3 (Core)Q13
0580/42/O/N/250580_w25_qp_42Oct/Nov 2025 · Paper 4 (Extended)Q7
0580/13/M/J/250580_s25_qp_13May/June 2025 · Paper 1 (Core)Q14

More IGCSE Maths 0580 Mensuration questions

Browse IGCSE Maths questions by topic

See every topic and subtopic on one page →

Book a free trial class

Tell us a little about your requirement.