Discia GCSE Maths › Geometry & Measures › Finding the Area of Any Triangle

Finding the Area of Any Triangle worksheet

8 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

8 questions 32 marks Sheet 1
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  1. 3 marks

    \(ABC\) is a triangle.

    Triangle ABC not accurately drawn, with the lengths of AB and CA and the angle between them at A given8 cm8 cmABC33°Diagram NOT accurately drawn

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

    Give your answer to 1 decimal place.

  2. 4 marks

    \(ABCD\) is a parallelogram.

    Parallelogram ABCD not accurately drawn, with AB and AD labelled, the angle at A given and the diagonal BD dashed14 cm11 cmABCD80°Diagram NOT accurately drawn

    Work out the area of the parallelogram.

    Give your answer correct to 1 decimal place.

  3. 4 marks

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

    Triangle ABC not accurately drawn, with the lengths of AB and CA given and the angle between them at A marked x8 cm10 cmABCxDiagram NOT accurately drawn

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

    Give your answer correct to 1 decimal place.

  4. 5 marks

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

    Quadrilateral ABCD not accurately drawn, with AB and CD labelled and the diagonal AC dashed and labelled12 cm13 cmABCD12 cmDiagram NOT accurately drawn

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

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

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

    Give your answer to 1 decimal place.

  5. 3 marks

    \(ABC\) is a triangle.

    Triangle ABC not accurately drawn, with the lengths of AB and CA and the angle between them at A given8 cm14 cmABC83°Diagram NOT accurately drawn

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

    Give your answer to 1 decimal place.

  6. 4 marks

    \(ABCD\) is a parallelogram.

    Parallelogram ABCD not accurately drawn, with AB and AD labelled, the angle at A given and the diagonal BD dashed15 cm8 cmABCD79°Diagram NOT accurately drawn

    Find the area of the parallelogram.

    Give your answer to 1 decimal place.

  7. 4 marks

    The area of triangle \(ABC\) is \(112.2\) cm².

    Triangle ABC not accurately drawn, with the lengths of AB and CA given and the angle between them at A marked x15 cm17 cmABCxDiagram NOT accurately drawn

    Work out the size of the acute angle marked \(x\).

    Give your answer to 1 decimal place.

  8. 5 marks

    Here is a quadrilateral \(ABCD\). The diagonal \(AC\) has been drawn.

    Quadrilateral ABCD not accurately drawn, with AB and CD labelled and the diagonal AC dashed and labelled13 cm9 cmABCD13 cmDiagram NOT accurately drawn

    \(AB = 13\) cm, \(CD = 9\) cm and \(AC = 13\) cm.

    Angle \(BAC = 28^\circ\) and angle \(DCA = 64^\circ\).

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

    Give your answer to 1 decimal place.

Answers

  1. \(17.4\ \text{cm}^2\)
  2. \(151.7\ \text{cm}^2\)
  3. \(62.9^\circ\)
  4. \(80.6\ \text{cm}^2\)
  5. \(55.6\ \text{cm}^2\)
  6. \(117.8\ \text{cm}^2\)
  7. \(61.6^\circ\)
  8. \(92.2\ \text{cm}^2\)

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