Question

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

• A. $24sqcm$
• B. $42sqcm$
• C. $154sqcm$
• D. $196sqcm$

Answer 1

Answer: (B)

$42sqcm$

Consider the figure shown.

Now, four sector of the circles inside the square forms a circle of radius = 7cm.

So, Area of shaded region or the area enclosed between the circumference = Area of square- Area of circle formed

Hence area enclosed between circumference $=\left({14}^2\right)-\left(\pi r^2\right)$

Area of the shaded region $=\left(196\right)-(\frac{22}{7}\times 7\times 7)$

$=42cm$