Every compound shapes and parts of shapes question from 4 Cambridge IGCSE Mathematics (0580) past papers (Oct/Nov 2025 to May/June 2026), syllabus section 5.5. 5 Core-tier questions. Each question is labelled with its question paper code (for example 0580/31/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 Compound Shapes and Parts of Shapes past paper questions: Core (Papers 1 and 3)
May/June 2026 · Paper 3 · 0580/31/M/J/26 · Q17
The diagram shows a circle inside a rectangle measuring 32 cm by 18 cm. The shaded area (the rectangle outside the circle) is 450 cm². Find the radius of the circle.
Show solution
- Area of the rectangle = 32 × 18 = 576 cm².
- The shaded part is the rectangle without the circle, so area of circle = 576 − 450 = 126 cm².
- Area of a circle = πr², so πr² = 126.
- Divide by π: r² = 126 ÷ π = 40.107…
- Square root: r = √40.107… = 6.333… = 6.33 cm (3 s.f.)
May/June 2026 · Paper 3 · 0580/32/M/J/26 · Q17(a,c)
The diagram shows a compound shape made from two rectangles. The top edge is 12 cm, the left edge is 6 cm, the right edge is 9 cm and the lower-left step is 7 cm.
(a) Work out the perimeter of the shape.
(c) A square has the same area as the compound shape. Calculate the side length of the square.
Show solution
- First find the two missing sides.
- Missing vertical side = 9 − 6 = 3 cm. Missing horizontal side = 12 − 7 = 5 cm.
- Add all six sides: 12 + 9 + 5 + 3 + 7 + 6 = 42 cm
- Find the area by taking the missing corner away from a full rectangle.
- Full rectangle = 12 × 9 = 108 cm². Missing corner = 7 × 3 = 21 cm².
- Area = 108 − 21 = 87 cm².
- A square with area 87 cm² has side √87 = 9.327… = 9.33 cm
May/June 2026 · Paper 3 · 0580/32/M/J/26 · Q20
A metal rectangle is 25 cm by 60 cm. 12 circles, each with radius 5 cm, are cut out of the metal. Calculate the percentage of the metal remaining.
Show solution
- Area of the rectangle = 25 × 60 = 1500 cm².
- Area of one circle = πr² = π × 5² = 25π cm². Twelve circles = 12 × 25π = 300π = 942.47… cm².
- Metal remaining = 1500 − 942.47… = 557.52… cm².
- Percentage remaining = 557.52…⁄1500 × 100 = 37.16…
- 37.2%
Oct/Nov 2025 · Paper 3 · 0580/32/O/N/25 · Q22
A garden is a 10 m by 16 m rectangle with a circular pond at one end. The diameter of the pond equals the width of the garden, and half of the pond sticks out beyond the rectangle. The shaded area is grass.
(a) Find the area of the pond. (b) Find the area of the grass. (c) Find the percentage of the garden that is grass.
Show solution
- The diameter equals the width of the garden, 10 m, so the radius is 5 m.
- Area of the pond = πr² = π × 5² = 25π = 78.53…
- 78.5 m²
- Half of the pond lies inside the rectangle, and that part is not grass.
- Rectangle = 10 × 16 = 160 m². Half the pond = 78.53… ÷ 2 = 39.26… m².
- Grass = 160 − 39.26… = 120.73… = 121 m²
- The whole garden is the rectangle plus the half of the pond that sticks out: 160 + 39.26… = 199.26… m².
- Percentage of grass = 120.73…⁄199.26… × 100 = 60.58…
- 60.6%
Oct/Nov 2025 · Paper 3 · 0580/33/O/N/25 · Q9
The diagram shows an L-shaped compound shape. The bottom is 23 cm, the right side is 12 cm, the top is 8 cm, the step down is 7 cm, the middle ledge is 15 cm and the left side is 5 cm.
Show solution
- Split the L-shape into two rectangles with a horizontal line.
- Bottom rectangle: 23 cm long and 5 cm high, so its area = 23 × 5 = 115 cm².
- Top rectangle: 8 cm wide and 12 − 5 = 7 cm high, so its area = 8 × 7 = 56 cm².
- Total area = 115 + 56 = 171 cm²
- Check: 8 + 15 = 23 ✓ and 5 + 7 = 12 ✓, so the sides fit together.
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