MathDB

Each of the three large squares shown below is the same size. Segments that intersect the sides of the squares intersect at the midpoints of the sides. How do the shaded areas of these squares compare?
[asy] unitsize(36); fill((0,0)--(1,0)--(1,1)--cycle,gray); fill((1,1)--(1,2)--(2,2)--cycle,gray); draw((0,0)--(2,0)--(2,2)--(0,2)--cycle); draw((1,0)--(1,2)); draw((0,0)--(2,2));
fill((3,1)--(4,1)--(4,2)--(3,2)--cycle,gray); draw((3,0)--(5,0)--(5,2)--(3,2)--cycle); draw((4,0)--(4,2)); draw((3,1)--(5,1));
fill((6,1)--(6.5,0.5)--(7,1)--(7.5,0.5)--(8,1)--(7.5,1.5)--(7,1)--(6.5,1.5)--cycle,gray); draw((6,0)--(8,0)--(8,2)--(6,2)--cycle); draw((6,0)--(8,2)); draw((6,2)--(8,0)); draw((7,0)--(6,1)--(7,2)--(8,1)--cycle);
label("

I

",(1,2),N); label("

II

",(4,2),N); label("

III

",(7,2),N); [/asy]

\text{(A)}\ \text{The shaded areas in all three are equal.}

\text{(B)}\ \text{Only the shaded areas of }I\text{ and }II\text{ are equal.}

\text{(C)}\ \text{Only the shaded areas of }I\text{ and }III\text{ are equal.}

\text{(D)}\ \text{Only the shaded areas of }II\text{ and }III\text{ are equal.}

\text{(E)}\ \text{The shaded areas of }I, II\text{ and }III\text{ are all different.}

Problem Statement