MathDB

13

Part of 2008 AMC 12/AHSME

Problems(1)

Square - Triangle Region

Source: AMC 12 2008B Problem 13

2/29/2008
Vertex E E of equilateral △ABE \triangle{ABE} is in the interior of unit square ABCD ABCD. Let R R be the region consisting of all points inside ABCD ABCD and outside △ABE \triangle{ABE} whose distance from AD‾ \overline{AD} is between 13 \frac{1}{3} and 23 \frac{2}{3}. What is the area of R R? (A)\ \frac{12\minus{}5\sqrt3}{72} \qquad (B)\ \frac{12\minus{}5\sqrt3}{36} \qquad (C)\ \frac{\sqrt3}{18} \qquad (D)\ \frac{3\minus{}\sqrt3}{9} \qquad (E)\ \frac{\sqrt3}{12}
geometrytrapezoidrectangleAMC