Problem

The diagram shows a square $ABCD$ where each side has length 12 cm. Points $E$ and $F$ lie on the sides $BC$ and $CD$ respectively and are such that $BE = \frac{1}{3}BC$ and $DF = \frac{1}{3}DC$. The arc $EF$ is part of a circle with centre $A$. The shaded region is bounded by the arc $EF$ and the line segments $EC$ and $FC$.

(a) Show that the size of angle $EAF$ is 0.9273 radians, correct to 4 significant figures.

(b) Find the perimeter of the shaded region.

(c) Find the area of the shaded region.