Question

A triangle has sides with lengths: 14, 9, and 7. How do you find the area of the triangle using Heron's formula?

Answer 1

The area A is `12*sqrt(5)`

Explanation:

Heron's formula: `A=sqrt(s(s-a)(s-b)(s-c)`, where s, semiperimeter, is `(a+b+c)/2`

Applying the formula:
`s=(14+9+7)/2=30/2=15`
`A = sqrt (15*(15-14)(15-9)(15-7))`
`A= sqrt (15*1*6*8)=sqrt(720)=12*sqrt(5)`