Date: / / A circle of radius $6$ cm is inscribed in a square. Find the area of the shaded region.

Step 1: Determine the side length of the square

When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. Since the radius of the circle is $6$ cm, the diameter is $2 \times 6 = 12$ cm. Therefore, the side length of the square is $12$ cm.

Step 2: Calculate the area of the square

The area of a square is calculated by squaring its side length. With a side length of $12$ cm, the area of the square is $12^2 = 144$ square cm.

Step 3: Calculate the area of the circle

The area of a circle is calculated using the formula $\pi r^2$, where $r$ is the radius. Given the radius is $6$ cm, the area of the circle is $\pi (6)^2 = 36\pi$ square cm.

Step 4: Calculate the area of the shaded region

The shaded region is the area of the square minus the area of the inscribed circle. So, we subtract the area of the circle from the area of the square: $144 - 36\pi$ square cm.

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