2024 CEMC Gauss (Grade 8) Problems/Problem 10

Problem

In the diagram, a square with side length $6$ is partially shaded.

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The largest shaded region is a square with side length $3$ . The other two shaded regions are squares with side lengths $2$ and $1$ . What is the total area of the unshaded region?

$\textbf{(A)}\ 12 \qquad\textbf{(B)}\ 18 \qquad\textbf{(C)}\ 22 \qquad\textbf{(D)}\ 24 \qquad\textbf{(E)}\ 30$

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 $6$ , its area is:

$6^2 = 36$

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

$3^2 = 9$

$2^2 = 4$

$1^2 = 1$

$9 + 4 + 1 = 14$

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

~anabel.disher

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2024 CEMC Gauss (Grade 8) Problems/Problem 10

Problem

Solution