Question

Four circles are described about the four corners of a square of side $7$ cm, so that each circle touches two others as shown in the figure. Find the area of the shaded region.

• A. $10.2$ sq. cm
• B. $10.5$sq. cm
• C. $12$ sq. cm
• D. $15.4$ sq. cm

Answer 1

The correct option is B $10.5$sq. cm

Given: side of the square $=7$ cm

Let $ABCD$ represent the given square of side $7$ cm.

Then, radius of each circle $=$ $\frac{\text{diameter}}{2}=\frac{7}{2}=3.5$ cm

Area of the shaded region $=$ Area of square $ABCD$ $-$ Area of four quadrants

$=$ ${\text{side}}^2-4\left(\frac{\pi r^2}{4}\right)$

$=[7\times 7-4\times (\frac{1}{4}\times \frac{22}{7}\times {3.5}^2)]$

$=$ $[49-38.5]$

$=10.5$ sq. cm