Heron's formula in Mathematics

Updated on September 3, 2025 | By Learnzy Academy

Heron's Formula is used to find the area of a triangle when you know the lengths of all three sides.

Let the three sides be:
a, b, and c

Step 1: Calculate the semi-perimeter (s):
s = (a + b + c) / 2

Step 2: Use Heron’s formula to find the area (A):
A = √[s × (s - a) × (s - b) × (s - c)]

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List of question on "Heron's formula"

  1. A triangular flower bed has sides measuring 18 meters, 24 meters, and 30 meters. A gardener wants to plant grass over it. How many square meters of grass is needed?
  2. A kite-shaped field is made of two congruent right triangles with sides 13 m, 12 m, and 5 m. Find the total area of the field.
  3. An equilateral triangle has an area of 81√3 cm². Find the length of each side using Heron’s formula.
  4. A triangle has an area of 84 cm² and its sides are in the ratio 7:8:9. Find the lengths of the sides.
  5. A triangle has sides of lengths a, b, and c, where a = 2√3 cm, b = 4 cm, and c = 2√3 cm. Find the area using Heron’s formula.
  6. A triangle has one side 17 cm, and the difference between the other two sides is 3 cm. If the perimeter is 42 cm, find the area.
  7. Find the area of an equilateral triangle with side length 10 cm using Heron’s formula.
  8. The sides of a triangular swimming pool are 30 m, 40 m, and 50 m. What is its surface area?
  9. For a triangle with sides of lengths 35 cm, 54 cm, and 61 cm, determine its area and the length of the altitude corresponding to the 54 cm side.
  10. A park is in the shape of a quadrilateral ABCD, where angle C is 90 degrees. The sides are: AB = 9 meters BC = 12 meters, CD = 5 meters, AD = 8 meters. How much area does the park occupy?
  11. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3:2. Find the area of the triangle.
  12. Calculate the area of a triangle with sides 35 cm, 54 cm, and 61 cm, and also find the length of its smallest altitude.
  13. Find the area of a parallelogram with adjacent sides of 60 m and 40 m and a diagonal of 80 m.
  14. A rhombus-shaped field with sides of 30 m and a longer diagonal of 48 m provides grazing grass for 18 cows. Calculate the area of grass available per cow.
  15. Find the area of a quadrilateral field ABCD where angle C is 90 degrees, AB = 9 meters, BC = 12 meters, CD = 5 meters and AD = 8 meters.
  16. The sides of a triangle are in the ratio of 12:17:25, and its perimeter is 540 cm. Find its area.
  17. Find the area of a triangle whose two sides are 18 cm and 10 cm, and the perimeter is 42 cm.
  18. Calculate the rent paid by a company that hired a triangular flyover wall for 3 months, given the wall's sides are 122 m, 22 m, and 120 m, and the advertisement rate is ₹5000 per m² per year.
  19. Determine the area of an isosceles triangle with a perimeter of 30 cm and equal sides measuring 12 cm each.