Heron's Formula:

Let us learn about Hero's Formula and understand this concept better:

In geometry, Heron's (or Hero's) formula, named after Hero of Alexandria, states that the area A of a triangle whose sides have lengths a, b, and c is

where s is the semiperimeter of the triangle:

Heron's formula can also be written as:

Let us now look at one example of Heron's Formula:

Heron formula reduce the form on left to (ch)², or (cb)² − (cd)² from 4A ² = 4s(s − a)(s − b)(s − c). On the right side using b ² − d ² = h ² by the Pythagorean theorem.We get the form like,

(s(s − a) + (s − b)(s − c))² − (s(s − a) − (s − b)(s − c))²

Using this form (p + q) ² − (p − q) ² = 4pq.

cb = s(s-a) + (s-b)(s-c) and cd = s(s-a) - (s-b) (s-c).

Hope you like the above example of Heron's Formula.
Please leave your comments, if you have any doubts.