<p>please enlighten me!</p>
<p>In the figure ImageShack®</a>; - Online Photo and Video Hosting, arc SBT is one quarter of a circle with center R and radius 6. If the length plus the width of rectangle ABCR is 8, then the perimeter of of the shaded region is</p>
<p>(A) 8 + 3π
(B) 10 + 3π
(C) 14 + 3π
(D) 1 + 6π
(E) 12 + 6π</p>
<p>The line segment RB is a radius of the (quarter) circle, so its length is 6. This is a diagonal of the rectangle ABCR, so AC (also a diagonal of ABCR) also has a length of 6. The length of SR plus the length of RT is 12; the non-shaded perimeter of that is given as 8 (length plus width of the rectangle), so the shaded perimeter is 12-8 = 4. The perimeter of a circle is 2<em>pi</em>r, so the perimeter of a quarter of a circle is (1/2)<em>pi</em>r. The perimeter of this particular quarter-circle is (1/2)<em>pi</em>6 = 3pi.</p>
<p>The perimeter of the shaded region is thus 6 + 4 + 3pi = 10 + 3pi. The answer is B.</p>
<p>Where is this question from? If not the BB (blue book, aka The Official SAT Study Guide), I recommend using only BB and other College Board–released material.</p>
<p>Crazybandit, this question’s from the BB.</p>
