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What is Heron’s Formula?

Maths | 7-14 yrs | Interactive

Heron’s formula, sometimes known as Hero’s formula is named after Hero of Alexandria, a mathematician, and engineer in 10 AD.

Definition for Heron’s formula

Heron’s formula gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas that calculate the area of a triangle. The area can be calculated using all the three sides, especially in scalene triangle, where none of the sides are equal. Most formulas use the height of a triangle to calculate the area.

What are the steps for Heron’s formula?

According to this formula,

Area of the triangle –

A = \sqrt{s(s-a)(s-b)(s-c)},

where the semi – perimeter of the triangle,

s=\frac{a+b+c}{2}.

a, b, c are the lengths of the sides of the triangle.

Heron’s Formula Worksheet

1. Calculate the semiperimeter of a triangle, s, where a = 23, b = 40, c = 35.

a. 35
b. 48
c. 25
d. 49
Right Answer- d. 49

2. Calculate the area of a triangle using Heron’s formula, if the three sides of the triangle are, a = 5, b = 9, c = 6

a. 12.34
b. 10.6
c. 14.14
d. 13.26
Right Answer- 14.14

3. Calculate the side of a triangle b, if side a = 12 and side c = 6 and the semi – perimeter equals 13.
a. 9
b. 8
c. 6
d. 7
Right Answer- b. 8

3 Interesting facts about Heron’s Formula

  1. Heron’s formula has been known to mathematicians for nearly 2000 years.
  2. Proof of this formula can be found in Hero of Alexandria’s book “Metrica”.
  3. Many mathematicians believe that Archimedes already knew the formula before Heron. Some also believe that this formula has Vedic roots and the credit should be given to the ancient Hindus.
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