ABCD is a square, E and F are the midpoints of sides CD and BC, respectively. What is the ratio of the shaded region area to unshaded region?
A. 1 : 1
B. 2 : 1
C. 3 : 1
D. 5 : 3
E. 8 : 3
The OA is D.
I know that the area of the square is L^2, and the area of the shaded region will be the sum of areas of the two triangles,
The area of the bigest triangle will be,
1/2* L^2, because b = h
Then, the area of the smallest triangle will be,
1/2*(L^2)/4
The area of the shaded region will be,
1/2*L^2 + 1/8*L^2 = 5/8*L^2
The area of unshaded region will be
L^2 - 5/8*L^2 = 3/8*L^2
Finally, Shaded region / unshaded region will be,
$$\frac{5/8*L^2\ }{3/8*L^2}=\frac{5}{3}$$
Is there a strategic approach to this question? Because I think that this is the long way to solve it. Can any experts help? Thanks!
