Is this even a type of question that would appear on the SAT?

Test Preparation SAT Preparation
1

<p>Excuse the shoddy Paint sketch:
<a href="http://i44.tinypic.com/1sd4ht.jpg%5B/url%5D"&gt;http://i44.tinypic.com/1sd4ht.jpg&lt;/a>
In square ABCD above, the shaded region is the intersection of two circular regions centered at B and D, respectively. If AB=10, then the area of the shaded region is
A. 25(pi-2)
B. 50(pi-2)
C. 25pi
D. 50pi
E. 40pi(5-sqrt2)</p>

<p>Seeing as a quarter of the circle is 25pi, I have eliminated C, D, and E. But, I don't know the proper way to solve this, and it's irritating me. The reason I think this might not be a SAT-type question because Princeton Review tells me to "ballpark" for this question, so I think they might have just made it up to force me to guess. I hate dumb strategies like this; I hate having to guess even if my odds are 50-50. If you do know the right way to solve this, could you explain?
If that curve was a clean exponential like 2^x or e^x, I could do LRAM or RRAM to estimate the area, but obviously Calculus is not the way to go on the SAT, especially with a process about as annoying and tedious as Newton's Method.</p>

2

<p>Venn diagram to the rescue!
area of the square = (area of the first sector) + (area of the second sector) - (common shaded area)
(see <a href="http://talk.collegeconfidential.com/sat-preparation/631013-sat-math-question-help.html#post1061593817%5B/url%5D"&gt;http://talk.collegeconfidential.com/sat-preparation/631013-sat-math-question-help.html#post1061593817&lt;/a&gt;).
100 = (2)(pi)10^2/4 - x
x = 50pi - 100,
x = 50(pi - 2).</p>