[discia] GCSE Maths › Geometry & Measures › Area and Perimeter

Area and Perimeter

discia.org 10 questions · 32 marks
Name Date
  1. Either paper 4 marks

    Here is a rectangle.

    16 cm7 cm
    (a)

    Find the perimeter of the rectangle.

    (b)

    Find the area of the rectangle.

    Show answer
    (a) \(46\ \text{cm}\)
    (b) \(112\ \text{cm}^2\)
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  2. Either paper 2 marks

    Here is a triangle. The dashed line is the perpendicular height.

    20 cm10 cm

    Work out the area of the triangle.

    Show answer
    \(100\ \text{cm}^2\)
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  3. Either paper 4 marks

    Here is a rectangle with an area of \(12\) cm².

    x cm4 cmDiagram NOT accurately drawn
    (a)

    Work out the length of the side marked \(x\).

    (b)

    Work out the perimeter of the rectangle.

    Show answer
    (a) \(3\ \text{cm}\)
    (b) \(14\ \text{cm}\)
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  4. Either paper 4 marks

    The diagram shows a right-angled triangle.

    12 cm20 cm16 cmDiagram NOT accurately drawn
    (a)

    Find the perimeter of the triangle.

    (b)

    Find the area of the triangle.

    Show answer
    (a) \(48\ \text{cm}\)
    (b) \(96\ \text{cm}^2\)
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  5. Either paper 2 marks

    The diagram shows an isosceles triangle.

    14 cm16 cm

    Find the perimeter of the triangle.

    Show answer
    \(46\ \text{cm}\)
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  6. Either paper 4 marks

    The diagram shows a parallelogram.

    17 cm15 cm12 cm
    (a)

    Work out the area of the parallelogram.

    (b)

    Work out the perimeter of the parallelogram.

    Show answer
    (a) \(204\ \text{cm}^2\)
    (b) \(64\ \text{cm}\)
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  7. Either paper 3 marks

    The square below has an area of \(121\) cm².

    x cm
    (a)

    Find the length of the side marked \(x\).

    (b)

    Find the perimeter of the square.

    Show answer
    (a) \(11\ \text{cm}\)
    (b) \(44\ \text{cm}\)
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  8. Either paper 4 marks

    Here is a regular decagon.

    5 cm
    (a)

    Calculate the perimeter of the decagon.

    (b)

    A different regular decagon has a perimeter of \(70\) cm.

    Calculate the length of one of its sides.

    Show answer
    (a) \(50\ \text{cm}\)
    (b) \(7\ \text{cm}\)
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  9. Either paper 2 marks

    Here is a rectangular carpet that measures 11 m by 9 m.

    11 m9 mDiagram NOT accurately drawn

    Part of the carpet is covered by a square rug of side 3 m.

    Show that \(\frac{ 1 }{ 11 }\) of the carpet is covered by the rug.

    Show answer
    \(\frac{ 3^2 }{ 11 \times 9 } = \frac{ 9 }{ 99 } = \frac{ 1 }{ 11 }\)
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  10. Either paper 3 marks

    Callum is trying to find the area of this rectangle.

    5 cm8 cm5 cm8 cm

    Callum writes, "The area is 26 cm² because 5 + 8 + 5 + 8 = 26".

    (a)

    Explain what is wrong with Callum's method.

    (b)

    Sofia works out the area of a different shape. Her answer is 110 cm.

    Explain why her answer cannot be fully correct.

    (c)

    Calculate the correct area of Callum's rectangle.

    Show answer
    (a) Callum added all four sides, which gives the perimeter (the distance round the edge) and not the area. The area is length × width = 5 × 8 = 40 cm², not 26 cm².
    (b) cm is a unit of length, but an area is measured in square units, so the answer should be 110 cm².
    (c) \(40\ \text{cm}^2\)
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discia.org Area and Perimeter · sheet 1
Answers Area and Perimeter · sheet 1
  1. (a) \(46\ \text{cm}\)
    (b) \(112\ \text{cm}^2\)
  2. \(100\ \text{cm}^2\)
  3. (a) \(3\ \text{cm}\)
    (b) \(14\ \text{cm}\)
  4. (a) \(48\ \text{cm}\)
    (b) \(96\ \text{cm}^2\)
  5. \(46\ \text{cm}\)
  6. (a) \(204\ \text{cm}^2\)
    (b) \(64\ \text{cm}\)
  7. (a) \(11\ \text{cm}\)
    (b) \(44\ \text{cm}\)
  8. (a) \(50\ \text{cm}\)
    (b) \(7\ \text{cm}\)
  9. \(\frac{ 3^2 }{ 11 \times 9 } = \frac{ 9 }{ 99 } = \frac{ 1 }{ 11 }\)
  10. (a) Callum added all four sides, which gives the perimeter (the distance round the edge) and not the area. The area is length × width = 5 × 8 = 40 cm², not 26 cm².
    (b) cm is a unit of length, but an area is measured in square units, so the answer should be 110 cm².
    (c) \(40\ \text{cm}^2\)
discia.org Area and Perimeter · sheet 1