Now that we know the side length of the square is 12 cm, we can calculate its area using the formula for the area of a square, which is side squared.

Next, we calculate the area of the inscribed circle using the formula π r². We are given the radius r = 6 cm and instructed to use π = (22)/(7).

A circle of radius $6 \, \text{cm}$ is inscribed in a square. Find the area of the shaded region.

Answer: The area of the shaded region is $\frac{216}{7} \text{ cm}^2$ .

Step-by-step solution

Step 1: Determine the side 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 is given as $6 \text{ cm}$ , the diameter will be $2 \times 6 \text{ cm}$ .

Step 2: Calculate the area of the square

Now that we know the side length of the square is $12 \text{ cm}$ , we can calculate its area using the formula for the area of a square, which is side squared.

Step 3: Calculate the area of the circle

Next, we calculate the area of the inscribed circle using the formula $\pi r^2$ . We are given the radius $r = 6 \text{ cm}$ and instructed to use $\pi = \frac{22}{7}$ .

Step 4: Calculate the area of the shaded region

The shaded region is the area of the square minus the area of the circle. We subtract the calculated area of the circle from the area of the square to find the final answer.

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A circle of radius 6 cm6 \, \text{cm}6cm is inscribed in a square. Find the area of the shaded region.