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<p>I got the answer 32 (A), however, the answer key say's it's 64 (C)</p>
<p>I got it by doing 1/2 * x * x root 3 = 16 root 3</p>
<p>x= 5.656854249</p>
<p>Then area of square = (5.656854249)^2= 32</p>
<p>Can someone explain what I did wrong?</p>
<p>In your first step, change the 1/2 to a 1/4…Did you forget the 1/2 in 1/2 base times height?</p>
<p>No, but why do you multiply 1/2 by 1/2?</p>
<p>All I did was apply the formula: 1/2 *the base which is X * the height which is x root 3</p>
<p>If you let the base equal x, the height is actually x root 3 /2 this can be seen by splitting the triangle into two 30-60-90 triangles each with base x/2 and hypotenuse x. Applying the pythagorean theorem makes this problem trivial.</p>