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Plane Mensuration practice questions — GCSE Maths

16 free multiple-choice problems on plane mensuration, ordered to match GCSE Maths difficulty, each with a full worked solution. No account needed — and there's a fresh problem set every day.

Problems & worked solutions

Problem #0869 UK GCSE

Problem 1 — Plane Mensuration

A rectangle of area 30 cm230\text{ cm}^2 has a square of area 4 cm24\text{ cm}^2 cut out. The remaining area is:

Show answer & worked solution
  1. A. 26 cm226\text{ cm}^2✓ correct
  2. B. 34 cm234\text{ cm}^2
  3. C. 120 cm2120\text{ cm}^2
  4. D. 30 cm230\text{ cm}^2

30−4=26 cm230 - 4 = 26\text{ cm}^2.

Problem #0870 UK GCSE

Problem 2 — Plane Mensuration

An L-shape has outer edges of length 6,4,2,2,4,66, 4, 2, 2, 4, 6 cm. Its perimeter is:

Show answer & worked solution
  1. A. 2424 cm✓ correct
  2. B. 1212 cm
  3. C. 4848 cm
  4. D. 2020 cm

6+4+2+2+4+6=246 + 4 + 2 + 2 + 4 + 6 = 24 cm.

Problem #0873 UK GCSE

Problem 3 — Plane Mensuration

A rectangle is 55 cm by 33 cm. Its area is:

Show answer & worked solution
  1. A. 15 cm215\text{ cm}^2✓ correct
  2. B. 16 cm216\text{ cm}^2
  3. C. 8 cm28\text{ cm}^2
  4. D. 30 cm230\text{ cm}^2

A=5×3=15 cm2A = 5 \times 3 = 15\text{ cm}^2.

Problem #0872 UK GCSE

Problem 4 — Plane Mensuration

A rectangle is 55 cm by 33 cm. Its perimeter is:

Show answer & worked solution
  1. A. 1616 cm✓ correct
  2. B. 1515 cm
  3. C. 88 cm
  4. D. 3030 cm

P=2(5+3)=16P = 2(5 + 3) = 16 cm.

Problem #0871 UK GCSE

Problem 5 — Plane Mensuration

A garden is a 1010 m by 66 m rectangle with a 22 m by 22 m square pond. The grass area is:

Show answer & worked solution
  1. A. 56 m256\text{ m}^2✓ correct
  2. B. 60 m260\text{ m}^2
  3. C. 64 m264\text{ m}^2
  4. D. 52 m252\text{ m}^2

10×6−2×2=60−4=56 m210 \times 6 - 2 \times 2 = 60 - 4 = 56\text{ m}^2.

Problem #0866 UK GCSE

Problem 6 — Plane Mensuration

A circle has radius 77 cm. Its circumference (in terms of π\pi) is:

Show answer & worked solution
  1. A. 14π14\pi cm✓ correct
  2. B. 49π49\pi cm
  3. C. 7π7\pi cm
  4. D. 28π28\pi cm

C=2π×7=14πC = 2\pi \times 7 = 14\pi cm.

Problem #0863 UK GCSE

Problem 7 — Plane Mensuration

A sector has a central angle of 90∘90^\circ. What fraction of the whole circle is it?

Show answer & worked solution
  1. A. 14\tfrac{1}{4}✓ correct
  2. B. 12\tfrac{1}{2}
  3. C. 90100\tfrac{90}{100}
  4. D. 190\tfrac{1}{90}

90360=14\dfrac{90}{360} = \dfrac{1}{4}.

Problem #0860 UK GCSE

Problem 8 — Plane Mensuration

A semicircle is what fraction of a full circle?

Show answer & worked solution
  1. A. 12\tfrac{1}{2}✓ correct
  2. B. 14\tfrac{1}{4}
  3. C. 13\tfrac{1}{3}
  4. D. 1360\tfrac{1}{360}

A semicircle is half a circle, 12\tfrac{1}{2}.

Problem #0862 UK GCSE

Problem 9 — Plane Mensuration

A semicircle has radius 1010 cm. Its arc length (in terms of π\pi) is:

Show answer & worked solution
  1. A. 10π10\pi cm✓ correct
  2. B. 20π20\pi cm
  3. C. 5π5\pi cm
  4. D. 100π100\pi cm

12×2π×10=10π\tfrac{1}{2} \times 2\pi \times 10 = 10\pi cm.

Problem #0868 UK GCSE

Problem 10 — Plane Mensuration

An L-shape splits into two rectangles of area 12 cm212\text{ cm}^2 and 8 cm28\text{ cm}^2. Its total area is:

Show answer & worked solution
  1. A. 20 cm220\text{ cm}^2✓ correct
  2. B. 4 cm24\text{ cm}^2
  3. C. 96 cm296\text{ cm}^2
  4. D. 40 cm240\text{ cm}^2

12+8=20 cm212 + 8 = 20\text{ cm}^2.

6 more Plane Mensuration questions in the app

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