Construct a square ABCD. Let E be the midpoint of CD. The line segment AE intersects the diagonal BD at F.
A. List all the polygons formed by segments BD and AE in the square.
B. What percent of the area of the square ABCD is the area of each of the polygons formed?
C. What if E is 1/4 of its way from C to D? What percent of the area of the square will be the area of the three triangles (ABF, ADF, DEF) and the quadrilateral (BCEF)? How about 1/3? 2/3? Is there are relationship?

Construct a square ABCD. Let E be the midpoint of CD. The line segment AE intersects the diagonal BD at F.
A. List all the polygons formed by segments BD and AE in the square.
B. What percent of the area of the square ABCD is the area of each of the polygons formed?
C. What if E is 1/4 of its way from C to D? What percent of the area of the square will be the area of the three triangles (ABF, ADF, DEF) and the quadrilateral (BCEF)? How about 1/3? 2/3? Is there are relationship?