Question

The square of side 14 cm is circumscribed. Then the area of the shaded region is: 

• A. 12 cm\(^2\)
• B. 14 cm\(^2\)
• C. 144 cm\(^2\)
• D. 196 cm\(^2\)

Hint:

Subtract the area of the inscribed circle from the area of the square to get shaded region.

Answer 1

The Correct Option is C

We are given:

The side of the square is \( 14 \, \text{cm} \)
A circle is inscribed inside the square

Step 1: Area of the square \[ \text{Area}_{\text{square}} = 14 \times 14 = 196 \, \text{cm}^2 \] Step 2: Radius of the inscribed circle \[ \text{Radius } r = \frac{14}{2} = 7 \, \text{cm} \] Step 3: Area of the circle \[ \text{Area}_{\text{circle}} = \pi r^2 = \pi \times 7^2 = 154 \, \text{cm}^2 \quad (\text{Use } \pi \approx 22/7) \] Step 4: Area of the shaded region \[ \text{Shaded} = \text{Area}_{\text{square}} - \text{Area}_{\text{circle}} = 196 - 154 = \boxed{144 \, \text{cm}^2} \]