The area of a circle is calculated using the formula π r², where r is the radius. Given the radius r = 7 cm, and using π = (22)/(7), we can find the area of the circle.

Length of square $= 2r$ Area of square $= (2r)^2 = (2 \times 7)^2 = 14^2 = 196 \text{ cm}^2$ Area of Circle $= \pi r^2 = \frac{22}{7} \times 7^2 = \frac{22 \times 7 \times 7}{7} = 22 \times 7 = 154 \text{ cm}^2$ $196 - 154 = 42 \text{ cm}^2$ (square, circle, area, radius, difference)

Answer: The area of the shaded region is $42 \text{ cm}^2$ .

Step-by-step solution

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 $r$ is given as $7$ cm, the diameter is $2 \times 7 = 14$ cm. Therefore, the side of the square is $14$ cm.

Step 2: Calculate the area of the square

The area of a square is calculated by squaring the length of its side. With the side length determined as $14$ cm, we can now calculate the area of the square.

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 $r = 7$ cm, and using $\pi = \frac{22}{7}$ , we can find the area of the circle.

Step 4: Calculate the area of the shaded region

The shaded region represents the area of the square that is not covered by the inscribed circle. To find this area, we subtract the area of the circle from the area of the square.

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