[discia] GCSE Maths › Geometry & Measures › Area of Compound Shapes

Area of Compound Shapes

discia.org 10 questions · 43 marks
Name Date
  1. Either paper 3 marks

    Shape \(ABCDE\) is drawn on a centimetre grid.

    xyABCDE
    (a)

    Complete this statement by writing the name of one side of the shape.

    \(AB : \_\_\_\_\_\_ = 3 : 1\)

    (b)

    On the centimetre grid below, draw a rectangle with the same area as shape \(ABCDE\).

    xy
    Show answer
    (a) CD (or DC)
    (b) Any rectangle of area \(14\) cm\(^2\), for example \(2\) cm by \(7\) cm
    (b)xy
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  2. Either paper 5 marks

    Here is an L-shape. Every corner of the shape is a right angle.

    The dashed line splits it into two rectangles.

    10 cm4 cm6 cm10 cm4 cm14 cmDiagram NOT accurately drawn
    (a)

    Calculate the area of the shape.

    (b)

    Calculate the perimeter of the shape.

    Show answer
    (a) \(80\ \text{cm}^2\)
    (b) \(48\ \text{cm}\)
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  3. Either paper 5 marks

    Here is a shape made from two rectangles. Every corner is a right angle.

    17 cm14 cm9 cmx cmy cm7 cmDiagram NOT accurately drawn
    (a)

    Calculate the length marked \(x\).

    (b)

    Calculate the length marked \(y\).

    (c)

    Calculate the area of the shape.

    Show answer
    (a) \(7\ \text{cm}\)
    (b) \(8\ \text{cm}\)
    (c) \(182\ \text{cm}^2\)
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  4. Either paper 5 marks

    Ben is covering the floor of his hallway with carpet. The floor is the L-shape below, and every corner is a right angle.

    10 m5 m6 m6 m4 m11 mDiagram NOT accurately drawn
    (a)

    Calculate the area of the floor.

    (b)

    The carpet cost £10 for each square metre.

    Work out how much he pays.

    Show answer
    (a) \(74\ \text{m}^2\)
    (b) \(\text{£}740\)
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  5. Either paper 6 marks

    The diagram shows a shape with two vertical sides. The dashed line splits it into a rectangle and a right-angled triangle.

    12 cm28 cm20 cm12 cmDiagram NOT accurately drawn
    (a)

    Work out the perimeter of the shape.

    (b)

    Work out the area of the shape.

    Show answer
    (a) \(72\ \text{cm}\)
    (b) \(240\ \text{cm}^2\)
    Another like this
  6. Either paper 5 marks

    The diagram shows a rectangle with a rectangular piece cut out of it.

    Every corner of the shape is a right angle.

    13 cm12 cm6 cm6 cm3 cm6 cm4 cm12 cmDiagram NOT accurately drawn
    (a)

    Work out the area of the shape.

    (b)

    Work out the perimeter of the shape.

    Show answer
    (a) \(138\ \text{cm}^2\)
    (b) \(62\ \text{cm}\)
    Another like this
  7. Either paper 3 marks

    The diagram shows a rectangle with a rectangular piece cut from one corner.

    All the corners are right angles. Measurements are in centimetres.

    20 cmx cm4 cm18 cmDiagram NOT accurately drawn

    The area of the shape is \(332\ \text{cm}^2\).

    Work out the value of \(x\).

    Show answer
    \(7\ \text{cm}\)
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  8. Either paper 3 marks

    Here is a compound shape made from two rectangles. All measurements are in centimetres.

    (3x + 9) cm(2x + 4) cm(2x + 5) cm(x + 4) cm(4x + 9) cmDiagram NOT accurately drawn

    Show that the area of the shape can be written as \(8x^2 + 43x + 56\) cm².

    Show answer
    \((3x + 9)(2x + 4) + (x + 4)(2x + 5) = 8x^2 + 43x + 56\)
    Another like this
  9. Either paper 3 marks

    Shape \(ABCDE\) is drawn on a centimetre grid.

    xyABCDE
    (a)

    Complete this statement by writing the name of one side of the shape.

    \(AB : \_\_\_\_\_\_ = 5 : 1\)

    (b)

    On the centimetre grid below, draw a rectangle with the same area as shape \(ABCDE\).

    xy
    Show answer
    (a) EA (or AE)
    (b) Any rectangle of area \(42\) cm\(^2\), for example \(6\) cm by \(7\) cm
    (b)xy
    Another like this
  10. Either paper 5 marks

    The diagram shows an L-shape. Every corner of the shape is a right angle.

    The dashed line splits it into two rectangles.

    10 cm6 cm5 cm5 cm5 cm11 cmDiagram NOT accurately drawn
    (a)

    Calculate the area of the shape.

    (b)

    Calculate the perimeter of the shape.

    Show answer
    (a) \(85\ \text{cm}^2\)
    (b) \(42\ \text{cm}\)
    Another like this
discia.org Area of Compound Shapes · sheet 1
Answers Area of Compound Shapes · sheet 1
  1. (a) CD (or DC)
    (b) Any rectangle of area \(14\) cm\(^2\), for example \(2\) cm by \(7\) cm
    (b)xy
  2. (a) \(80\ \text{cm}^2\)
    (b) \(48\ \text{cm}\)
  3. (a) \(7\ \text{cm}\)
    (b) \(8\ \text{cm}\)
    (c) \(182\ \text{cm}^2\)
  4. (a) \(74\ \text{m}^2\)
    (b) \(\text{£}740\)
  5. (a) \(72\ \text{cm}\)
    (b) \(240\ \text{cm}^2\)
  6. (a) \(138\ \text{cm}^2\)
    (b) \(62\ \text{cm}\)
  7. \(7\ \text{cm}\)
  8. \((3x + 9)(2x + 4) + (x + 4)(2x + 5) = 8x^2 + 43x + 56\)
  9. (a) EA (or AE)
    (b) Any rectangle of area \(42\) cm\(^2\), for example \(6\) cm by \(7\) cm
    (b)xy
  10. (a) \(85\ \text{cm}^2\)
    (b) \(42\ \text{cm}\)
discia.org Area of Compound Shapes · sheet 1