单选题
In the figure below, WXYZ is a square whose sides are 12. AB, CD, EF,
and GH are each 8, and are the diameters of the four semicircles. What is the
area of the shaded region?
【正确答案】
C
【答案解析】If you don't know how to solve this, you must use TACTIC 4 and guess after eliminating the absurd choices. Which choices are absurd? Certainly, A and B, both of which are negative. Also, since Choice D is about 94, which is much more than half the area of the square, it is much too big. Guess between Choice C (about 43) and Choice E (about 50). If you remember that the way to find shaded areas is to subtract, guess C.
**The area of the square is 122 = 144. The area of each semicircle is 8π, one-half the area of a circle of radius 4. So together the areas of the semicircles is 32π.
**The area of the square is 122 = 144. The area of each semicircle is 8π, one-half the area of a circle of radius 4. So together the areas of the semicircles is 32π.