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 $b$:
$b = \sqrt{[(-8)-3]^2+(6-4)^2} = \sqrt{125}$
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 verify that this is a right angle triangle:
$a^2+c^2 = 5^2+10^2 = 125 = b^2$
Thus, $b$ is the hypotenuse of this right angle triangle. Let angle B be the angle of $90^{\circ}$
We can find the area of the triangle:
$Area = \frac{1}{2}ac~sin~B$
$Area = \frac{1}{2}(5)(10)~sin~90^{\circ}$
$Area = \frac{1}{2}(5)(10)(1)$
$Area = 25$
