1978 AHSME Problems/Problem 29
Problem
Sides , , , and , respectively of convex quadrilateral are extended past , , , and to points , , , and . Also, , , , and , and the area of is 10. Find the area of .
Solution
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 [] = .
~ Mathavi
Note: Anyone with a diagram would be of great help (still new to LaTex).