Pre-calc simple question

Question

For the diagram below, you are given that BD = 10 and BE = 4. Compute the outer perimeter of the shaded region in terms of θ.

 

 

Here is the diagram: 

 

 

http://s12.postimg.org/x0qsemexp/math.png

Answer 1

Using Law of Sines:

 

AD / sin θ = 10 / sin (90 - θ)

AD = 10 sin θ / cos θ

 

Area ADB = 0.5(10)(10 sin θ / cos θ)

Area ADB = 50 sin θ / cos θ

 

Area of shaded = 40 + (50 sin θ / cos θ)