Find the area of triangle $SVW$

Question

To find length of side $SV$ I used Pythagoras theorem which gave $SV=17$. To find angle $SVW$ I added $45$ to $90 = 135$ to find side length $SW = 17^2+24^2-2 \cdot 17 \cdot 24 \cdot \cos135=37$ and lastly, to find area of the triangle I used Heron's formula $\sqrt{39(39-17)(39-24)(39-37)} = 160$ but the correct answer is $56.25$

Answer 1

It's $$\frac{24\cdot\sqrt{15^2+8^2}}{2}.$$

Answer 2

$SV$ is perpendicular to $WV$ and $SV=\sqrt{VT^2+ST^2}$.

The area of the triangle is given by $\frac12 \cdot SV \cdot WV$.