[discia] GCSE Maths › Geometry & Measures › Finding the Area of Any Triangle

Finding the Area of Any Triangle

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

    \(ABC\) is a triangle.

    8 cm8 cmABC33°Diagram NOT accurately drawn

    Work out the area of triangle \(ABC\).

    Give your answer to 1 decimal place.

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    \(17.4\ \text{cm}^2\)
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  2. Calculator 3 marks

    The area of triangle \(ABC\) is \(39\) cm².

    11 cmx cmABC44°Diagram NOT accurately drawn

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

    Give your answer correct to 1 decimal place.

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    \(10.2\ \text{cm}\)
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  3. Calculator 4 marks

    \(ABCD\) is a parallelogram.

    14 cm11 cmABCD80°Diagram NOT accurately drawn

    Find the area of the parallelogram.

    Give your answer correct to 1 decimal place.

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    \(151.7\ \text{cm}^2\)
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  4. Calculator 4 marks

    The area of triangle \(ABC\) is \(35.6\) cm².

    8 cm10 cmABCxDiagram NOT accurately drawn

    Calculate the size of the acute angle marked \(x\).

    Give your answer to 1 decimal place.

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    \(62.9^\circ\)
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  5. Calculator 5 marks

    The diagram shows a quadrilateral \(ABCD\). The diagonal \(AC\) has been drawn.

    12 cm13 cmABCD12 cmDiagram NOT accurately drawn

    \(AB = 12\) cm, \(CD = 13\) cm and \(AC = 12\) cm.

    Angle \(BAC = 26^\circ\) and angle \(DCA = 39^\circ\).

    Find the area of the quadrilateral \(ABCD\).

    Give your answer to 1 decimal place.

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    \(80.6\ \text{cm}^2\)
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  6. Calculator 5 marks

    \(ABC\) is a triangle. The lengths of all three of its sides are marked on the diagram.

    17 cm12 cm13 cmABCDiagram NOT accurately drawn

    Find the area of triangle \(ABC\).

    Give your answer to 1 decimal place.

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    \(77.8\ \text{cm}^2\)
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  7. Calculator 5 marks

    A triangular picnic area at a campsite has one side \(PQ\) of length \(14\) m.

    Angle \(QPR = 39^\circ\) and angle \(PQR = 56^\circ\).

    Find the area of the picnic area.

    Give your answer to the nearest square metre.

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    \(51\ \text{m}^2\)
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  8. Calculator 5 marks

    A regular hexagon has all of its vertices on a circle of radius \(13\) cm. The centre of the circle is \(O\).

    \(O\) is joined to every vertex, cutting the hexagon into six triangles.

    Work out the area of the hexagon.

    Give your answer to 1 decimal place.

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    \(439.1\ \text{cm}^2\)
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  9. Calculator 5 marks

    \(ABC\) is a triangle. Two of its sides and one of its angles are marked on the diagram.

    15 cm13 cmABC77°Diagram NOT accurately drawn

    Calculate the area of triangle \(ABC\).

    Give your answer correct to 1 decimal place.

    Show answer
    \(69.4\ \text{cm}^2\)
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  10. Calculator 4 marks

    The area of triangle \(ABC\) is \(62\) cm².

    Angle \(BAC = 119^\circ\).

    \(AB = x\) cm, and \(AC\) is four times as long as \(AB\).

    Work out the value of \(x\).

    Give your answer correct to 1 decimal place.

    Show answer
    \(6.0\)
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discia.org Finding the Area of Any Triangle · sheet 1
Answers Finding the Area of Any Triangle · sheet 1
  1. \(17.4\ \text{cm}^2\)
  2. \(10.2\ \text{cm}\)
  3. \(151.7\ \text{cm}^2\)
  4. \(62.9^\circ\)
  5. \(80.6\ \text{cm}^2\)
  6. \(77.8\ \text{cm}^2\)
  7. \(51\ \text{m}^2\)
  8. \(439.1\ \text{cm}^2\)
  9. \(69.4\ \text{cm}^2\)
  10. \(6.0\)
discia.org Finding the Area of Any Triangle · sheet 1