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

Area and Perimeter

discia.org 10 questions · 30 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 Higher1 mark

    A regular pentagon has sides of length \(2\) cm. Every side is made longer, so that each side is now \(6\) cm.

    Work out what the perimeter of the shape is multiplied by.

    Show answer
    \(\times 3\)
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  4. Either paper 4 marks

    Here is a rectangle with an area of \(54\) cm².

    x cm9 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) \(6\ \text{cm}\)
    (b) \(30\ \text{cm}\)
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  5. Either paper 4 marks

    The diagram shows a right-angled triangle.

    6 cm10 cm8 cmDiagram NOT accurately drawn
    (a)

    Find the perimeter of the triangle.

    (b)

    Find the area of the triangle.

    Show answer
    (a) \(24\ \text{cm}\)
    (b) \(24\ \text{cm}^2\)
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  6. Either paper 2 marks

    The diagram shows an isosceles triangle.

    13 cm14 cm

    Find the perimeter of the triangle.

    Show answer
    \(41\ \text{cm}\)
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  7. Either paper 4 marks

    The diagram shows a parallelogram.

    13 cm15 cm12 cm
    (a)

    Work out the area of the parallelogram.

    (b)

    Work out the perimeter of the parallelogram.

    Show answer
    (a) \(156\ \text{cm}^2\)
    (b) \(56\ \text{cm}\)
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  8. Either paper 3 marks

    The square below has an area of \(196\) cm².

    x cm
    (a)

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

    (b)

    Find the perimeter of the square.

    Show answer
    (a) \(14\ \text{cm}\)
    (b) \(56\ \text{cm}\)
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  9. Either paper 4 marks

    Here is a regular octagon.

    12 cm
    (a)

    Calculate the perimeter of the octagon.

    (b)

    A different regular octagon has a perimeter of \(64\) cm.

    Calculate the length of one of its sides.

    Show answer
    (a) \(96\ \text{cm}\)
    (b) \(8\ \text{cm}\)
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  10. Either paper 2 marks

    Here is a rectangular carpet that measures 8 m by 5 m.

    8 m5 mDiagram NOT accurately drawn

    Part of the carpet is covered by a square rug of side 2 m.

    Show that \(\frac{ 1 }{ 10 }\) of the carpet is covered by the rug.

    Show answer
    \(\frac{ 2^2 }{ 8 \times 5 } = \frac{ 4 }{ 40 } = \frac{ 1 }{ 10 }\)
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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. \(\times 3\)
  4. (a) \(6\ \text{cm}\)
    (b) \(30\ \text{cm}\)
  5. (a) \(24\ \text{cm}\)
    (b) \(24\ \text{cm}^2\)
  6. \(41\ \text{cm}\)
  7. (a) \(156\ \text{cm}^2\)
    (b) \(56\ \text{cm}\)
  8. (a) \(14\ \text{cm}\)
    (b) \(56\ \text{cm}\)
  9. (a) \(96\ \text{cm}\)
    (b) \(8\ \text{cm}\)
  10. \(\frac{ 2^2 }{ 8 \times 5 } = \frac{ 4 }{ 40 } = \frac{ 1 }{ 10 }\)
discia.org Area and Perimeter · sheet 1