Discia GCSE Maths › Geometry & Measures › Surface Area

Surface Area worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 32 marks Sheet 1
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  1. 2 marks

    The diagram shows a cube. The dashed lines are the edges you cannot see from this side.

    A cube drawn in isometric projection with one edge labelled 2 cm and its hidden edges dashed2 cm

    Each edge of the cube is \(2\) cm long.

    Find the total surface area of the cube.

  2. 3 marks

    Here is a cuboid.

    A cuboid drawn in isometric projection with its three dimensions labelled 9 cm, 7 cm and 5 cm9 cm7 cm5 cm

    Calculate the total surface area of the cuboid.

  3. 4 marks

    Here is a solid prism that is \(17\) cm long.

    A prism drawn in isometric projection whose end face is a right-angled triangle, with the length of the prism labelled 17 cm17 cm

    The cross-section of the prism is a right-angled triangle with sides \(5\) cm, \(12\) cm and \(13\) cm. The right angle is between the \(5\) cm side and the \(12\) cm side.

    Work out the total surface area of the prism.

  4. 3 marks

    Here is a cuboid with a rectangular base measuring \(9\) cm by \(7\) cm. Its height is \(h\) cm.

    A cuboid drawn in isometric projection with a base of 9 cm by 7 cm and its height labelled h cm9 cm7 cmh cm

    The total surface area of the cuboid is \(254\) cm².

    Find the value of \(h\).

  5. 4 marks

    The diagram shows a solid prism \(16\) cm long. Its cross-section is an isosceles triangle with a base of \(12\) cm and a perpendicular height of \(8\) cm.

    A triangular prism drawn in isometric projection, its end face an isosceles triangle of base 12 cm and perpendicular height 8 cm, with the prism 16 cm long8 cm12 cm16 cm
    (a)

    Find the length of one of the two sloping sides of the triangle.

    (b)

    Find the total surface area of the prism.

  6. 2 marks

    The diagram shows a cube. The dashed lines are the edges you cannot see from this side.

    A cube drawn in isometric projection with one edge labelled 3 cm and its hidden edges dashed3 cm

    Each edge of the cube is \(3\) cm long.

    Find the total surface area of the cube.

  7. 3 marks

    The diagram shows a cuboid.

    A cuboid drawn in isometric projection with its three dimensions labelled 2 cm, 5 cm and 3 cm2 cm5 cm3 cm

    Calculate the total surface area of the cuboid.

  8. 4 marks

    Here is a solid prism that is \(18\) cm long.

    A prism drawn in isometric projection whose end face is a right-angled triangle, with the length of the prism labelled 18 cm18 cm

    The cross-section of the prism is a right-angled triangle with sides \(3\) cm, \(4\) cm and \(5\) cm. The right angle is between the \(3\) cm side and the \(4\) cm side.

    Find the total surface area of the prism.

  9. 3 marks

    The diagram shows a cuboid with a rectangular base measuring \(3\) cm by \(6\) cm. Its height is \(h\) cm.

    A cuboid drawn in isometric projection with a base of 3 cm by 6 cm and its height labelled h cm3 cm6 cmh cm

    The total surface area of the cuboid is \(216\) cm².

    Calculate the value of \(h\).

  10. 4 marks

    Here is a solid prism \(7\) cm long. Its cross-section is an isosceles triangle with a base of \(16\) cm and a perpendicular height of \(6\) cm.

    A triangular prism drawn in isometric projection, its end face an isosceles triangle of base 16 cm and perpendicular height 6 cm, with the prism 7 cm long6 cm16 cm7 cm
    (a)

    Find the length of one of the two sloping sides of the triangle.

    (b)

    Find the total surface area of the prism.

Answers

  1. \(24\ \text{cm²}\)
  2. \(286\ \text{cm²}\)
  3. \(570\ \text{cm²}\)
  4. \(4\ \text{cm}\)
  5. (a) \(10\ \text{cm}\)
    (b) \(608\ \text{cm²}\)
  6. \(54\ \text{cm²}\)
  7. \(62\ \text{cm²}\)
  8. \(228\ \text{cm²}\)
  9. \(10\ \text{cm}\)
  10. (a) \(10\ \text{cm}\)
    (b) \(348\ \text{cm²}\)

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