1978 AHSME Problems/Problem 29
Sides and , respectively, of convex quadrilateral are extended past and to points and . Also, and ; and the area of is . The area of is
Notice that the area of is the same as that of (same base, same height). Thus, the area of is twice that (same height, twice the base). Similarly, [ ] = 2 [ ], and so on.
Adding all of these, we see that the area the four triangles around is twice [ ] + [ ] + [ ] + [ ], which is itself twice the area of the quadrilateral . Finally,  =  + 4  = 5  = .
Note: Anyone with a diagram would be of great help (still new to LaTex).