AMC 10/12 Student Practice Questions
Guide to Student Practice Questions
Each of the following four large congruent squares is
subdivided into combinations of congruent triangles or
rectangles and is partially shaded. What percent of the total
area is partially shaded?
I
The original problem
and choices from the
2011 AMC 8 contest
(A) 12 (B) 20
(C) 25 (D) 33 (E) 37

Notice how each congruent square is divided into four equal parts. Since each square has four parts and there are four squares, there are [tex]16[/tex] of these parts in total. Because each of these parts make up [tex]\frac{1}{4}[/tex] of each square, all parts are equal. Therefore, you can count the total number of shaded parts to get your percentage.

The top left and bottom right both have one part shaded each for a total of [tex]2[/tex] parts.

The top right and bottom left have [tex]0.5[/tex] and [tex]1.5[/tex] parts shaded, respectively, for a total of [tex]2[/tex] parts.

Therefore, in total, there are [tex]2+2=4[/tex] parts shaded out of [tex]16[/tex] total parts.

Thus, the percentage of the total area that is shaded is:

[tex]\frac{4}{16}=\frac{1}{4}=\fbox{$25\%$}[/tex].