Question

ABCD is a square of side 14 cm with centers at A, B, C and D. Four circles are drawn in such a way that each circle touches externally two of the remaining three circles as shown below:


What is the area of the darker shaded region?

• A. $42{\mathrm{cm}}^2$
• B. $50{\mathrm{cm}}^2$
• C. $43{\mathrm{cm}}^2$
• D. $52{\mathrm{cm}}^2$

Answer 1

The correct option is A $42{\mathrm{cm}}^2$

Side of square = 14 cm
Four quadrants are present on the four sides of the square.
Therefore, radius of the circle = 14/2 cm = 7cm.
Area of the square ABCD$=14*14{\mathrm{cm}}^2=196{\mathrm{cm}}^2$

Area of each quadrant$=\frac{\pi r^2}{4{\mathrm{cm}}^2}=(22/7\times 7*7)/4{\mathrm{cm}}^2=77/2{\mathrm{cm}}^2$

So, Area of the four quadrants $=4\times 77/2{\mathrm{cm}}^2=154{\mathrm{cm}}^2$

So, Area of the darker shaded region = Area of the square ABCD - Area of the four quadrants $=196-154=42{\mathrm{cm}}^2$