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Year 9 Maths — Heron's formula

Find the area of a triangle from its three sides, without knowing its height.

Name: ________________________

  1. 1.A triangle with sides of 6, 8 and 10 cm has an area of 24 square cm. Taking the side of 10 cm as the base, what is the height, in centimetres?

  2. 2.A triangle has sides of 5, 12 and 13 cm. What is its area, in square centimetres?

  3. 3.A triangle has sides of 9, 12 and 15 cm. What is its area, in square centimetres?

  4. 4.A triangle has sides of 13, 14 and 15 cm. What is its area, in square centimetres?

  5. 5.A triangle has sides of 7, 24 and 25 cm. What is its area, in square centimetres?

  6. 6.A triangle has sides of 3, 4 and 5 cm. What is its semi-perimeter, in centimetres?

  7. 7.Sort each set of three lengths by whether a triangle can be built from them at all.

    Groups: A triangle is possible · No triangle is possible

    • 4, 4 and 20
    • 3, 4 and 5
    • 1, 2 and 3
    • 5, 12 and 13
    • 7, 24 and 25
    • 2, 3 and 9

  8. 8.A triangle has sides of 3, 4 and 5 cm. What is its area, in square centimetres?

Answer key — Year 9 Maths — Heron's formula

  1. 1. 4.8
  2. 2. 30
  3. 3. 54
  4. 4. 84
  5. 5. 84
  6. 6. 6
  7. 7. 3, 4 and 5 → A triangle is possible; 1, 2 and 3 → No triangle is possible; 5, 12 and 13 → A triangle is possible; 2, 3 and 9 → No triangle is possible; 7, 24 and 25 → A triangle is possible; 4, 4 and 20 → No triangle is possible
  8. 8. 6