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 $\pi = \frac{22}{7}$)

The square ABCD has side = 14 cm with four circles of equal radius $r$ centered at corners A, B, C, and D. The circles touch each other externally.

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When two circles touch externally, the distance between their centers equals the sum of their radii.

Since all circles have the same radius $r$:

Distance between adjacent centers = $r + r = 2r$

The centers are at the corners of the square, so the distance between adjacent centers equals the side of the square:

$2r = 14$

$r = 7$ cm

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Each circle's center is at a corner of the square, so only a quarter (90° sector) of each circle lies inside the square.

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Area of one quarter-circle = $\frac{1}{4} \times \pi r^2$

Total area of four quarter-circles inside the square:

Total circular area = $4 \times \frac{1}{4} \times \pi r^2$

$= \pi r^2$

$= \frac{22}{7} \times 7 \times 7$

$= \frac{22}{7} \times 49$

$= 22 \times 7$

$= 154$ cm²

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Area of square = $14^2 = 196$ cm²

Shaded Area = Area of Square - Area of Circular Portions

Shaded Area = $196 - 154$

$= 42$ cm²

Therefore, the area of the shaded region is 42 cm².