# Find the area of triangle $SVW$

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 $$56.25$$

• The area of SVW=0.5 * area of RSVW. – Nosrati Jun 20 at 6:52
• $VW$ is perpendicular to the plane holding $TSQV$. So the angle between $VW$ and any line in the plane through $V$ is $90^\circ$. In particular, $\angle SVW = 90^\circ$. – achille hui Jun 20 at 8:27
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## 2 Answers

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

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

• 0.5*17*24=204 ? still not 56.25 – Tiffany Jun 20 at 8:54
• The answer is probably incorrect then. – Epiksalad Jun 20 at 9:53

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