how do you find

Find the area of circle segment IK. To find the segment area, you need the area of triangle IDK so you can subtract it from the area of sector IDK. Draw an altitude straight down from D to segment IK. That creates two 30°- 60°- 90° triangles.

$\begin{array} \ \frac{\text{area of sector}}{\text{area of circle}}&=&\frac{\text{measure of central angle of sector}}{\text{total angular measure of circle}} \\~\\ \text{area of sector} &=& \frac{\text{measure of central angle in radians}}{2\pi}*(\pi r^2) \\~\\ \text{area of sector} &=&\frac{\text{measure of central angle in radians}}{2}*r^2 \end{array}$

As for segment area, I don't really know. LiamisHere's answer may help on that! 

Segment area formula

$A=\pi r^2*\frac{m^{\circ}}{360}-\frac{1}{2}bh$

One more "formula" 

Segment area  =

(1/2 ) R^2 (θ) - (1/2) R^2 sin (θ)  =

(1/2) R^2   [ θ -  sin ( θ) ]       where  θ  is the measure - in radians - of the central angle  of the sector