Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 35, 28, and 21 units in length?

Answer 1

`294` `"units"^2`

Explanation:

First, determine the semiperimeter `s` of the triangle (which has sides `a,b,c`).

`s=(a+b+c)/2`

We know that `a=35,b=28,c=21` so

`s=(35+28+21)/2=42`

Plug these into Heron's formula, which determines the area of a triangle:

`A=sqrt(s(s-a)(s-b)(s-c))`

`A=sqrt(42(42-35)(42-28)(42-21))`

`A=sqrt(42xx7xx14xx21)`

`A=sqrt(2^2xx3^2xx7^4)`

`A=2xx3xx7^2`

`A=294`