Heron’s Formula

Heron’s formula is named after Hero of Alexendria. Heron’s formula is a formula that can be used to find the area of a triangle, when given its three side lengths.

Heron’s formula

The area of a triangle whose side lengths are a,b and c is given by

A = √s(s−a)(s−b)(s−c)

where s semi-perimeter of the triangle.
s = (perimeter of the triangle)2
s = (a + b + c)2


Example1: Use Heron’s formula to find the area of triangle ABC, if AB=3,BC=2,CA=4
Step 1: Calculate the semi perimeter, S
s = (3 + 2 + 4)2 = 4.5

Step 2: Area of triangle

A = √s(s−a)(s−b)(s−c)

A = √4.5(4.5−3)(4.5−2)(4.5−4)
A = √8.437
A = 2.9

Example2:Given △ABC, with an area of 8.94 square units, a perimeter of 16 units and side lengths AB=3 and CA=7, what is BC ?
Given s = 16 units , A = 8.94 square units
s = perimeter2 = 162
s = 8
Using Heron’s formula,
A = √S(S−AB)(S−BC)(S−CA)
8.94 = √8(8−3)(8−BC)(8−7)
8.94 = √8(5)(8−BC)(1)
square both sides
8.942 = 8(5)(8−BC)(1)
79.9236 = 40(8−BC)
BC = 6

I hope, this article will help you a lot to understand the Heron’s formula, in solving various problems related to this article, if you still have any doubts related to this article, you can ask it into the comment section. If you have any problem with any topic of mathematics you can post your problem in the comment section. You will get a reply shortly.

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