jmc

Question

In the figure shown, arc ADB and arc BEC are semicircles, each with a radius of one unit. Point D, point E and point F are the midpoints of arc ADB, arc BEC and arc DFE, respectively. If arc DFE is also a semicircle, what is the area of the shaded region? FIGURE

Accepted Answer

Mark segments BF and DE and label their intersection P. Now, slide sector FPE on to sector DB and slide sector FPD on to sector EB. The shaded region is now a rectangle with side lengths 1 and 2, thus the area of the shaded region is 2.