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Class 9 Maths — Heron's formula

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

Name: ________________________

  1. 1.Heron's formula is the one to reach for when you know...

    • a) two sides and the angle between them
    • b) the perimeter and nothing else
    • c) all three sides but no height
    • d) the base and the height

  2. 2.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?

  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 5, 12 and 13 cm. What is its area, in square centimetres?

  5. 5.Each card gives a triangle's three sides. Put them in order of area, smallest first.

    • 6, 8 and 10
    • 9, 12 and 15
    • 3, 4 and 5
    • 13, 14 and 15

  6. 6.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

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

  7. 7.For a triangle with sides a, b and c, the semi-perimeter s is...

    • a) (a + b + c) ÷ 2
    • b) (a × b × c) ÷ 2
    • c) (a + b + c) ÷ 3
    • d) a + b + c

  8. 8.A triangle has sides of 13, 14 and 15 cm. What is its semi-perimeter, in centimetres?

Answer key — Class 9 Maths — Heron's formula

  1. 1. c) all three sides but no height
  2. 2. 4.8
  3. 3. 54
  4. 4. 30
  5. 5. 1. 3, 4 and 5 2. 6, 8 and 10 3. 9, 12 and 15 4. 13, 14 and 15
  6. 6. 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
  7. 7. a) (a + b + c) ÷ 2
  8. 8. 21