Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 4, 6, and 3 units in length?

Answer 1

`"Area"_triangle~~5.3` sq.units
(see below for use of Heron's formula)

Explanation:

Heron's formula tells us how to calculate the area of a triangle given the lengths of it's three sides.

If (for the general case) the lengths of the three sides are `a, b, and c` and the semi-perimeter is `s=(a+b+c)/2`

Then
`color(white)("XXX")"Area"_triangle=sqrt(s(s-a)(s-b)(s-c))`

For the given triangle with sides `4, 6, and 3`
`color(white)("XXX")s=13/2`
and
`color(white)("XXX")"Area"_triangle = sqrt((13/2)(13/2-4)(13/2-6)(13/2-3))`

`color(white)("XXXXXXX")=sqrt(13/2xx5/2xx1/2xx7/2)`

`color(white)("XXXXXXX")=sqrt(455)/4`

`color(white)("XXXXXXX")~~5.3` sq.units