im stuck with this problem?

Question

The figure below shaded in gray is that of a trapezoid having base length a and slant height b.

http://i181.photobucket.com/albums/x85/ctti_3/untitled-28.jpg

Answer 1

If you "chop" the triangle from one end and stick it on the other, the resulting rectangle is b*cos() by a=b*sin() wide, so #c.

Answer 2

Extend the two vertical lines so you divide the trapezoid into a rectangle and two congruent (by AAS) right triangles with hypotenuse b. The height of the triangles is the side adjacent to θ, so it is b cos θ, and the base is b sin θ. So the total area is
A(θ) = a (b cos θ) + 2 (1/2) (b sin θ) (b cos θ)
= b cos θ (a + b sin θ).
So answer 3 is correct.