Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 7, 15, and 9 units in length?

Answer 1

Area `~~43.39` sq. units.

Explanation:

Heron's formula tells us that the area of a triangle with sides `a, b, and c` is
`color(white)("XXX")"Area"_triangle=sqrt(s(s-a)(s-b)(s-c))`
where `s` is the semi-perimter (`(a+b+c)/2`).

In this case we have
`color(white)("XXX")a=7 color(white)("XX")b=15 color(white)("XX")c=9 and color(white)("XX")s=31/2`

So
`Area"_triangle = sqrt(31/2xx17/2xx1/2xx13/2)`

`color(white)("XXXX")~~41.39`