<p>I found this one challenging, mainly because it concerned perimeter, not area.</p>
<ul>
<li>Start with the length of the arc. - perimeter of a circle, divided by four (= 3pi)</li>
<li>Find the lengths of SA and CT. (lengths of radii, minus the length of AR and RC (12 - 8 = 4)</li>
</ul>
<p>Up to this point, I had no problem. At this moment, you have 4 + 3pi. However, I'm having trouble with finding AC. The answer of this problem should be B. 10 + 3pi, but I can't figure out the respective lengths of AR and RC.</p>
<ul>
<li><p>Find the length of AC. - Using L = 5 and W = 3 - (Both must be less than 6; and equal to 8 when added together, or 2L + 2W = 16) - use the Pythagorean theorem to get: AC = sqRt(34).</p></li>
<li><p>Add everything together to get 4 + sqRt(34) + 3pi = 9.831 + 3pi, which is closest to B.</p></li>
</ul>
<p>If they only gave us the area of rectangle ABCR, it'd be more easily solvable. I'll keep trying, and see if I can get it later.</p>
<p>If you think about it, AR MUST BE 5, and RC MUST BE 3. There are no other combinations which fit it. it can't be six, because it's shorter than the radius, but it can't be four either, because that would make it a square. So, I think you're right AeroEngineer. The answer doesn't come exactly as the choices are shown.</p>