Square ABCD has area 200. Point E lies on side ¯BC. Points F and G are the midpoints of ¯AE and ¯DE, respectively. Given that quadrilateral BEGF has area 34, what is the area of triangle GCD?
We can use coordinates. A = (0,sqrt(200)), B = (sqrt(200),sqrt(200)), C= (sqrt(200),0), D = (0,0). Then G = (sqrt(200)/2,17), E = (sqrt(200),34), F = (sqrt(200),17), so the area of triangle GCD is 45.
+180 
