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Area of Compound Shapes 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 52 marks Sheet 1
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  1. 5 marks

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

    The dashed line splits it into two rectangles.

    L-shape with all six sides labelled and a dashed line splitting it into two rectangles12 cm5 cm4 cm8 cm8 cm13 cmDiagram NOT accurately drawn
    (a)

    Work out the area of the shape.

    (b)

    Work out the perimeter of the shape.

  2. 5 marks

    The diagram shows a shape made from two rectangles. Every corner is a right angle.

    L-shape with four sides labelled, two sides marked x and y, and a dashed split line13 cm15 cm8 cmx cmy cm3 cmDiagram NOT accurately drawn
    (a)

    Work out the length marked \(x\).

    (b)

    Work out the length marked \(y\).

    (c)

    Work out the area of the shape.

  3. 5 marks

    Tomas is covering the floor of his garden with turf. The floor is the L-shape below, and every corner is a right angle.

    L-shaped floor plan in metres with a dashed line splitting it into two rectangles9 m3 m4 m4 m5 m7 mDiagram NOT accurately drawn
    (a)

    Work out the area of the floor.

    (b)

    The turf cost £8 for each square metre.

    Calculate how much he pays.

  4. 6 marks

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

    Four-sided shape with two vertical sides, split by a dashed line into a rectangle and a triangle12 cm10 cm13 cm5 cmDiagram NOT accurately drawn
    (a)

    Calculate the perimeter of the shape.

    (b)

    Calculate the area of the shape.

  5. 5 marks

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

    Every corner of the shape is a right angle.

    A rectangle with a rectangular notch cut out of its top edge, every side labelled13 cm11 cm6 cm3 cm4 cm3 cm3 cm11 cmDiagram NOT accurately drawn
    (a)

    Find the area of the shape.

    (b)

    Find the perimeter of the shape.

  6. 5 marks

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

    The dashed line splits it into two rectangles.

    L-shape with all six sides labelled and a dashed line splitting it into two rectangles12 cm5 cm6 cm5 cm6 cm10 cmDiagram NOT accurately drawn
    (a)

    Find the area of the shape.

    (b)

    Find the perimeter of the shape.

  7. 5 marks

    The diagram shows a shape made from two rectangles. Every corner is a right angle.

    L-shape with four sides labelled, two sides marked x and y, and a dashed split line12 cm16 cm4 cmx cmy cm5 cmDiagram NOT accurately drawn
    (a)

    Work out the length marked \(x\).

    (b)

    Work out the length marked \(y\).

    (c)

    Work out the area of the shape.

  8. 5 marks

    Leila is covering the floor of her patio with paving slabs. The floor is the L-shape below, and every corner is a right angle.

    L-shaped floor plan in metres with a dashed line splitting it into two rectangles9 m4 m5 m5 m4 m9 mDiagram NOT accurately drawn
    (a)

    Calculate the area of the floor.

    (b)

    The paving slabs cost £12 for each square metre.

    Calculate how much she pays.

  9. 6 marks

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

    Four-sided shape with two vertical sides, split by a dashed line into a rectangle and a triangle9 cm19 cm15 cm7 cmDiagram NOT accurately drawn
    (a)

    Work out the perimeter of the shape.

    (b)

    Work out the area of the shape.

  10. 5 marks

    Here is a rectangle with a rectangular piece cut out of it.

    Every corner of the shape is a right angle.

    A rectangle with a rectangular notch cut out of its top edge, every side labelled15 cm13 cm7 cm6 cm5 cm6 cm3 cm13 cmDiagram NOT accurately drawn
    (a)

    Work out the area of the shape.

    (b)

    Work out the perimeter of the shape.

Answers

  1. (a) \(124\ \text{cm}^2\)
    (b) \(50\ \text{cm}\)
  2. (a) \(12\ \text{cm}\)
    (b) \(5\ \text{cm}\)
    (c) \(135\ \text{cm}^2\)
  3. (a) \(47\ \text{m}^2\)
    (b) \(\text{£}376\)
  4. (a) \(40\ \text{cm}\)
    (b) \(90\ \text{cm}^2\)
  5. (a) \(131\ \text{cm}^2\)
    (b) \(54\ \text{cm}\)
  6. (a) \(90\ \text{cm}^2\)
    (b) \(44\ \text{cm}\)
  7. (a) \(11\ \text{cm}\)
    (b) \(8\ \text{cm}\)
    (c) \(104\ \text{cm}^2\)
  8. (a) \(56\ \text{m}^2\)
    (b) \(\text{£}672\)
  9. (a) \(50\ \text{cm}\)
    (b) \(117\ \text{cm}^2\)
  10. (a) \(165\ \text{cm}^2\)
    (b) \(68\ \text{cm}\)

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