(a) ABCDEF is a hexagon in which $$AB=BC=CD=DE=2$$ and $$EF=FA=1$$. Its interior angle C is between $$90^\circ$$ and $$180^\circ$$ and F is greater than $$180^\circ$$. The rest of the angles are $$90^\circ$$ each. What is its area?
(b) A convex polygon with n sides has all angles equal to $$150^\circ$$, except one angle. List all possible values of n.

For part (a), the hexagon splits into two trapeziums FEDC and FABC, each with parallel sides 1 and 2 and height 2, so each has area $$\frac{1}{2}(1+2)\times 2 = 3$$, giving a total hexagon area of $$3+3=6$$. For part (b), using the angle sum $$(n-1)\times 150^\circ + x = (n-2)\times 180^\circ$$ gives $$n = 7+\frac{x}{30}$$, and since the polygon is convex the odd angle x must satisfy $$0 < x < 180^\circ$$ and be a multiple of $$30^\circ$$, so $$x=30^\circ,60^\circ,90^\circ,120^\circ$$ giving $$n=8,9,10,11$$.