To find the area of the shaded region, we first need to understand the arrangement of the circles and the square. The circles are arranged so that they touch each other externally, and their centers are at the vertices of the square ABCD. Given:

• Side of the square, \(s = 14 \, \text{cm}\)

The radius of each circle is half of the side of the square because the centers of two touching circles (such as A and B) are 14 cm apart, which is equal to one side of the square ABCD. Therefore:

• Radius of each circle, \(r = \frac{14}{2} = 7 \, \text{cm}\)

Next, we calculate the area of the shaded region formed by the intersection of the four circles. The shaded area is the area of the square minus the sum of the areas of the four quarter circles in each corner of the square.

Step 1: Calculate the area of the square:

• \(\text{Area of the square} = s^2 = 14^2 = 196 \, \text{cm}^2\)

Step 2: Calculate the area of one circle:

• \(\text{Area of one circle} = \pi r^2 = \frac{22}{7} \times 7^2 = 154 \, \text{cm}^2\)

Step 3: Calculate the area of the four quarter circles inside the square:

• \(\text{Area of four quarter circles} = 4 \times \frac{1}{4} \times \text{Area of one circle} = \text{Area of one circle} = 154 \, \text{cm}^2\)

Step 4: Calculate the shaded area:

• \(\text{Shaded area} = \text{Area of the square} - \text{Area of four quarter circles} = 196 - 154 = 42 \, \text{cm}^2\)

On reviewing, we notice a mistake in the available answer choices. The correct calculation suggests that the shaded area should be 42 cm² rather than the provided solution of 24 cm².

Therefore, the correct answer should be 42 cm².