## Trigonometry (11th Edition) Clone

$Area = 25$
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: $Area = \sqrt{S(S-a)(S-b)(S-c)}$ $Area = \sqrt{13.09(13.09-5)(13.09-11.18)(13.09-10)}$ $Area = \sqrt{625}$ $Area = 25$