GCSE · Perimeter, area & volume

Area of triangles, parallelograms & trapeziaExam-style questions

Why every straight-sided area formula is a rectangle in disguise — base times PERPENDICULAR height, the trapezium average, compound shapes by splitting or subtracting, and why 1 m² is 10 000 cm².

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4
  1. 1
    Anil is going to tile the kitchen floor shown in the diagram.5.2 m0.5 m4.5 m1.6 mTiles are sold in boxes.

    One box of tiles covers 1.51.5 m² of floor.

    Anil buys 1616 boxes of tiles.

    He assumes that none of the tiles will be wasted.
    (a) Using this assumption, does Anil have enough tiles for the whole floor?

    You must show all your working.

    (4 marks)

    In fact, 10%10\% of the tiles Anil buys are wasted when he cuts them to fit.
    (b) Does this affect your answer to part (a)?

    You must give a reason for your answer.

    (1 mark)
    Level 3 · 5 marksTry it
  2. 2
    The diagram shows a plan of Cara's patio.

    The patio is a rectangle with a semicircle at each end.6 m3 mCara is going to cover the patio with one coat of sealant.

    Sealant is sold in tins.

    One tin of sealant covers 44 m²
    (a) Work out how many tins of sealant Cara needs.

    (4 marks)

    Cara then decides to cover the patio with two coats of sealant.
    (b) How does this affect your answer to part (a)?

    (1 mark)
    Level 3 · 5 marksTry it
  3. 3
    The diagram shows the plan of a flower bed, PQRSPQRS.9 m6 mPQRSPQRSPQRS is a trapezium.

    PQ=9PQ = 9 m

    PS=6PS = 6 m

    The area of the flower bed is 7272 m²

    Work out the perimeter of the flower bed.

    Give your answer correct to 33 significant figures.

    (5 marks)
    Level 3 · 5 marksTry it
  4. 4
    The diagram shows the plan of a floor.12 m5 m7 m9 mDiagram NOT accurately drawn

    (a) Work out the area of the floor.

    (b) Work out the perimeter of the floor.
    Level 3 · 4 marksTry it
  5. 5
    The diagram shows a parallelogram.9 cm7.5 cm6 cmDiagram NOT accurately drawn

    Work out the area of the parallelogram.
    Level 3 · 2 marksTry it

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