Question

A triangle has sides with lengths: 7, 2, and 15. How do you find the area of the triangle using Heron's formula?

Answer 1

`=42.43`

Explanation:

As per Heron's formula
Area of a triangle with sides `a`;`b`; and `c`
`A=sqrt(s(s-a)(s-b)(s-c))`
where `s` is half perimeter of the triangle and is given by
`s=(a+b+c)/2`
So we have
`a=7` ;`b=2` and `c=15`
Therefore Perimeter of the triangle
`s=(7+2+15)/2`
or
`s=24/2`
or
`s=12`
Area of the triangle
`A=sqrt(s(s-a)(s-b)(s-c))`
`=sqrt(12(12-7)(12-2)(12-15))`
`=sqrt(12(5)(10)(3)`
`=sqrt1800`
`=42.43`