Four equal circles are described about the four corners of a square so that each circle touches two of the others. Find the area of the space enclosed between the circumferences of the circles, each side of the square measuring 14 cm.

Since each side of square measures 14 cm, so the radius of each circle is half of the side.

Therefore, radius of circle, R = 7 cm

We need to find the area of the shaded region,

There is a quadrant of each of four circles that is present inside the square,

⇒ A_Q = 38.5 sq.cm

Also, area of square, A_S = 14² = 196 sq.cm

Area of shaded region = A_S – [4 × A_Q]

⇒ 196 – [4 × 38.5]

⇒ 196 – 154

⇒ 42 sq.cm

∴ area of shaded region is 42 sq. cm