Four circles of equal radius are drawn with centers, A, B, C and D such that ABCD is a square of side 14 cm and the circles touch externally as in the figure. The area of the shaded region bounded by the 4 circles is: (Take $π =\frac{22}{7}$).

$42\, cm^2$

The correct answer is Option (2) → $42\, cm^2$

Given:

• ABCD is a square of side 14 cm
• Four equal circles are drawn with centers at A, B, C, D such that each touches the adjacent circles externally
• π = 22/7
• Find the shaded area in the middle.

Step 1: Radius of the circles

Since ABCD is a square of side 14 cm, and the circles touch externally, the distance between centers of adjacent circles = side of the square = 14 cm.

$\text{Radius of each circle} = \frac{\text{side of square}}{2} = \frac{14}{2} = 7 \text{ cm}$

Step 2: Area of the square

$\text{Area of square} = 14 \times 14 = 196 \text{cm}^2$

Step 3: Area of the four quarter circles inside the square

• Each corner has a quarter circle (since the center is at the corner)
• Total area of 4 quarter circles = area of 1 full circle

$\text{Area of 1 circle} = \pi r^2 = \frac{22}{7} \times 7^2 = \frac{22}{7} \times 49 = 154 \text{cm}^2$

Step 4: Area of the shaded region

• The shaded area = area of square − area covered by the 4 quarter circles

$\text{Shaded area} = 196 - 154 = 42 \text{cm}^2$