How do you calculate the area of the shaded region?
Drop a vertial line from A to DC and call the point of intesection E
Now you have a rectangle AECB and a triangle ADE
You can find the lengths of AE and DE using trigonometry
You can find the length of EC useing subtraction
So now you can find the the 2 areas.
Add them and you have the area of the whole lot.
The area of the sector is (50/360)* pi*r^2
Find that and then subtract to get the shaded area.