Answer
$Area = 25$
Work Step by Step
Let $a$ be the length of the side from (0,0) to (3,4). We can find $a$:
$a = \sqrt{3^2+4^2} = 5$
Let $b$ be the length of the side from (3,4) to (-8,6). We can find $b$:
$b = \sqrt{[(-8)-3]^2+(6-4)^2} = \sqrt{125} = 11.18$
Let $c$ be the length of the side from (-8,6) to (0,0). We can find $c$:
$c = \sqrt{(-8)^2+6^2} = 10$
We can find the semiperimeter of the triangle:
$S = \frac{a+b+c}{2}$
$S = \frac{5+11.18+10}{2}$
$S = 13.09$
We can use Heron's formula to find the area of the triangle:
$Area = \sqrt{S(S-a)(S-b)(S-c)}$
$Area = \sqrt{13.09(13.09-5)(13.09-11.18)(13.09-10)}$
$Area = \sqrt{625}$
$Area = 25$
