If we know the lengths of all three sides, we can solve for area using Heron's formula.
First we need to find half of the perimeter. We will call it s:
[tex]s= \frac{35+35+12}{2}=41 [/tex]
Now we know sides a, b, and c, as well as s. Now just plug they values into the following formula:
[tex]A= \sqrt{s(s-a)(s-b)(s-c)} [/tex]
[tex]A= \sqrt{41(41-35)(41-35)(41-12)} [/tex]
[tex]A= \sqrt{41(6)(6)(29)} = 206.89 [/tex]
The area is 206.89
