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.