The area of a circle is calculated using the formula π r², where r is the radius. We will use the value of π = (22)/(7) for this calculation.

Side of sq $= 2r$ $= 14$ Area of sq $= 14^2 = 196 \text{ cm}^2$ Area of circ $= \pi r^2$ $= \frac{22}{\cancel{7}} \times \cancel{7} \times 7 = 154 \text{ cm}^2$ Area of shaded region $= \text{Area of sq} - \text{Area of circle}$ $= 196 - 154 = 42 \text{ cm}^2$ . (area, square, circle, radius, shaded region)

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

Step-by-step solution

Step 1: Determine the radius of the inscribed circle

When a circle is inscribed in a square, the diameter of the circle is equal to the side of the square. Therefore, the radius of the circle is half the side of the square. Given that the side of the square is $14$ cm, we can calculate the radius.

Step 2: Calculate the area of the square

The area of a square is calculated by squaring the length of its side. Given the side of the square is $14$ cm, we can find its area.

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. We will use the value of $\pi = \frac{22}{7}$ for this calculation.

Step 4: Calculate the area of the shaded region

The shaded region is the area of the square that is not covered by the circle. Therefore, we subtract the area of the circle from the area of the square to find the area of the shaded region.

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