Question

A triangle has sides with lengths: 14, 8, and 12. How do you find the area of the triangle using Heron's formula?

Answer 1

Area of triangle is `47.906`

Explanation:

Heron's formula for area of triangle having three sides as `a`, `b` and `c` is given by

`sqrt(s(s-a)(s-b)(s-c)` where `s=1/2(a+b+c)`

Here three sides are 14, 8 and 12. Thus `s=1/2(14+8+12)` i.e. `s=17`. Hence `s-a=3`, `s-b=9` and `s=c=5`.

Hence area of triangle is `sqrt(17*3*9*5` or `sqrt 2295` or `47.906`.