(a)[2]
Show that the measure of angle $EAF$ is $0.9273$ radians, correct to $4$ significant figures.
(b)[3]
Find the perimeter of the shaded region.
(c)[3]
Find the area of the shaded region.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram depicts a square $ABCD$ with each side measuring $12\ \text{cm}$. The points $E$ and $F$ are located on the sides $BC$ and $CD$ respectively, and satisfy $BE = \frac{1}{3}BC$ and $DF = \frac{1}{3}DC$. The arc $EF$ is a segment of a circle centred at $A$. The shaded region is enclosed by the arc $EF$ and the line segments $EC$ and $FC$.