Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `7`, `4`, and `7`?

Answer 1

`"Area"_triangle = 6sqrt(5)`

Explanation:

Heron's formula says that for a triangle with sides of length `a, b, c` and semi-perimeter `s=(a+b+c)/2`

`"Area"_triangle = sqrt(s(s-a)(s-b)(s-c))`

For the specified triangle
`color(white)("XXX")a=7`
`color(white)("XXX")b=4`
`color(white)("XXX")c=7`
`rarrcolor(white)("XXX")s=9`

`"Area"_triangle = sqrt(9(2)(5)(2)) = sqrt(3^3xx2^2xx5) = 6sqrt(5)`