4
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Can you find the area of the following square given the known lengths?

Good luck!

puzzle square

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  • $\begingroup$ just checking: did you make this yourself? $\endgroup$ – Omega Krypton Sep 17 at 1:50
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    $\begingroup$ No. I've been sent this problem by a friend, but I do not have the original source. $\endgroup$ – Dmitry Kamenetsky Sep 17 at 1:51
  • $\begingroup$ This is a classic puzzle. $\endgroup$ – greenturtle3141 Sep 17 at 3:52
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The diagonal of the square is

$\sqrt{(9+3)^2+5^2} = \sqrt{169} = 13$

so the area of the square is

$(\frac{13}{\sqrt{2}})^2 = \frac{169}{2}$

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  • $\begingroup$ OMG that is so brilliant! No mucking around with trigonometry and simultaneous equations with multiple unknowns. THANK YOU! $\endgroup$ – Dmitry Kamenetsky Sep 17 at 2:15
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    $\begingroup$ My pleasure. :) $\endgroup$ – Jens Sep 17 at 2:17

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