Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 8, and 22 units in length?

Answer 1

Heron's formula:
`color(white)("XXX")Area_triangle = sqrt(s(s-a)(s-b)(s-c))`

Explanation:

`s` is semi-perimeter `=(a+b+c)/2` for a triangle with sides `a, b, c`

For the given triangle with `a=25, b=8, and c=22`
`color(white)("XXX")s= 27.5`
and
`color(white)("XXX")Area_triangle = sqrt(27.5(2.5)(19.5)(5.5))`

`color(white)("XXXXXXX")=85.87` (approximately, using a calculator)