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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 $56.25$

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    $\begingroup$ The area of SVW=0.5 * area of RSVW. $\endgroup$ – Nosrati Jun 20 at 6:52
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    $\begingroup$ $VW$ 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, $\angle SVW = 90^\circ$. $\endgroup$ – achille hui Jun 20 at 8:27
  • $\begingroup$ This tutorial explains how to typeset mathematics on this site. $\endgroup$ – N. F. Taussig Jun 20 at 10:06
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$SV$ is perpendicular to $WV$ and $SV=\sqrt{VT^2+ST^2}$.

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

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    $\begingroup$ 0.5*17*24=204 ? still not 56.25 $\endgroup$ – Tiffany Jun 20 at 8:54
  • $\begingroup$ The answer is probably incorrect then. $\endgroup$ – Epiksalad Jun 20 at 9:53
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It's $$\frac{24\cdot\sqrt{15^2+8^2}}{2}.$$

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