View source for 2024 CEMC Gauss (Grade 8) Problems/Problem 10

== Problem==
In the diagram, a square with side length <math>6</math> is partially shaded.
{{Image needed}}
The largest shaded region is a square with side length <math>3</math>. The other two shaded regions are squares with side lengths <math>2</math> and <math>1</math>. What is the total area of the unshaded region?

<math> \textbf{(A)}\ 12 \qquad\textbf{(B)}\ 18 \qquad\textbf{(C)}\ 22 \qquad\textbf{(D)}\ 24 \qquad\textbf{(E)}\ 30 </math>
==Solution==
To find the unshaded area, we can subtract the shaded area from the total area.

Since the total area is represented by the [[square]] with length <math>6</math>, its area is:

<math>6^2 = 36</math>

We can find the area of each of the shaded squares as well, and add them together, giving us the total shaded area:

<math>3^2 = 9</math>

<math>2^2 = 4</math>

<math>1^2 = 1</math>

<math>9 + 4 + 1 = 14</math>

Thus, the unshaded area is <math>36 - 14 = \boxed {\textbf {(C) } 22}</math>.

~anabel.disher