SAT Math: More Shaded Region Problems

If you’ve read my recent post on Shaded Region problems and you’d like some more practice, try the problems below.  Remember, our strategy isn’t to try to find each of these areas directly, but rather to use the areas of the regions we know to help us determine the area of the shaded region that we want to find.  The relationship in these problems is:

$Area_{shaded}=Area_{whole}-Area_{unshaded}$

Good luck!  The answers appear at the bottom of this post.

1)  Two semicircles are drawn inside circle B.  These semicircles intersect at point B, which is the center of the larger circle.  The length of AC is 8.  What is the total area of the yellow shaded regions?

(A)  $8\pi$
(B)  $12\pi$
(C)  $16\pi$
(D)  $32\pi$
(E)  $48\pi$

2)  The square WXYZ has sides of length 15.  Three congruent squares are drawn inside the square as shown.  What is the total area of the gray shaded regions?

(A)  75
(B)  100
(C)  125
(D)  150
(E)  225

3)  Rectangle ADEH has an area of 84.  If AD = 12 and AB = BC = CD = GF, what is the total area of the green shaded regions?

(A)  56
(B)  60
(C)  64
(D)  70
(E)  77

4)  Circles AB, and C are congruent and tangent.  Triangle ABC was formed by connecting the centers of each of these circles.  If AC = 12, what is the area of the red shaded region inside the triangle?

(A)  $18$
(B)  $18\sqrt{3}-9\pi$
(C)  $18\sqrt{3}-18\pi$
(D)  $36\sqrt{3}-9\pi$
(E)  $36\sqrt{3}-18\pi$

If you have questions about these problems, the strategies used to solve “Shaded Region” problems, or anything else to do with the SAT, leave a comment or send me an email at info@cardinalec.com .

Solutions:
1)  (B)
2)  (D)
3)  (D)
4)  (E)