Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 8, 7, and 10 units in length?

Answer 1

`"Area"_triangle ~~27.81" sq. units"`

Explanation:

According to Heron's formula, for a triangle with sides of lengths `a, b,` and `c`
the area of the triangle is
`color(white)("XXX")"Area"_triangle =sqrt(s * (s-a) * (s-b) * (s-c))`

where `s` is the semi-perimeter; that is `s=(a+b+c)/2`

For a triangle with the given lengths `7, 8,` and `10`
`color(white)("XXX")s=12.5`
and
`color(white)("XXX")"Area"_triangle = sqrt(12.5 * 5.5 * 4.5 * 2.5)`

`color(white)("XXXXXXX")=sqrt(773.4375)`

`color(white)("XXXXXXX")~~27.81`