Question

(AMC8, 1994) Each of the three large squares shown below is the same size. Segments that intersect the sides of the squares intersect at midpoints of the sides. How do the areas of the shaded regions compare?

A. The shaded areas in all three are equal.
B. Only the shaded areas I and II are equal.
C. Only the shaded areas of I and III are equal.
D. Only the shaded areas of II and III are equal.
E. The shaded areas of I, II and III are all different.

Answer 1

A.

Explanation:

For square one, the dark part added up= 1/4 of the whole big square.

For square 2. the colored in part= 1/4 of the whole big square.

For square 3. The colored part = 1/4 of the whole big square.

Keep in mind that EACH OF THE SEGMENTS THAT INTERSECT THE SIDES OF THE SQUARES INTERSECT AT MIDPOINTS OF THE SIDES.

For number three, make sure to draw in what square two looks like. one line vertical, one horizontal.

THE ANSWER IS A THOUGH.