How do you solve this?

Question

In rectangle ABCD, point E is the midpoint of line segment BC. If the area of quadrilateral ABED is 2/3, what is the area of the rectangle ABCD?

They expect 11th graders to solve this on the SAT.

Answer 1

Draw F as the midpoint of AD right above E. Say ABCD has area x, then rectangle ABEF has area 1/2*x and triangle EFD has area 1/2*1/2x=1/4*x. Add these to get area ABED=2/3. So (1/2)x+(1/4)x=2/3 so 3/4*x=2/3, then multiply both sides by 4/3 to get x=4/3*2/3=8/9. Area of original ractangle is 8/9.

I guess they do expect 11 graders to solve this.

Answer 2

area of ABED
0.5*(BE+AD)*AB = 2/3
since E is the midpoint
2*BE = AD
0.5(BE+2*BE)*AB = 2/3
0.5*3*BE*AB = 2/3
BE*AB = 4/9

area of DEC = 0.5*EC*DC
since EC = BE
and DC = AB
area of DEC = 0.5*BE*AB
since BE*AB = 4/9
area of DEC = 0.5*4/9 = 2/9

area of ABCD = area of ABED +area of DEC
area of ABCD = 2/3 + 2/9 = 8/9