question_answer

Four identical semicircles are drawn inside a big square as shown in the figure. Each side of the big square is 14 cm long.

What is the area of the shaded region? (Use \[\pi =\frac{22}{7}\] )

A)  \[125\text{ }c{{m}^{2}}\]                  

B)  \[112\text{ }c{{m}^{2}}\]       

C)  \[173\text{ }c{{m}^{2}}\]                  

D)  \[159\text{ }c{{m}^{2}}\]

Correct Answer: B

Solution :

(b): Radius \[=14\text{ }cm\div 2=7cm\] Area of a  \[=\frac{1}{2}\times \frac{22}{7}\times 7\,\,cm\times 7\,\,cm\]                         \[=38.5\,\,c{{m}^{2}}\] Area of  \[=\frac{1}{2}\times 7\,\,cm\,\,\times 7\,\,cm=24.5\,\,c{{m}^{2}}\] Area of a  \[=38.5\,\,c{{m}^{2}}-24.5\,\,c{{m}^{2}}\]                             \[=14\,\,c{{m}^{2}}\] Area of shaded region \[=14\,c{{m}^{2}}\times 8=112\,\,c{{m}^{2}}\] Aliter Refer to Q.-10 again; Area (asked, here) \[=4\times \] standardized area as illustrated in solution to Q.-10. \[=4\times \frac{{{a}^{2}}}{2}[\pi -2]\] (where, a = length of one of the smaller squares)