question_answer

ABCD is a square park divided into 4 squares as shown in the figure. Semi-circular square beds are made as shown by the shaded portion. Find the area of the shaded region.   

A) \[75\text{ }{{m}^{2}}\]    

B)               \[76\text{ }{{m}^{2}}\]

C) \[\text{77 }{{m}^{2}}\]   

D) \[\text{189 }{{m}^{2}}\]

E) None of these

Correct Answer: C

Solution :

Explanation For each of the semicircle diameter \[= \,7 m.:\] \[\therefore  \,\,radius =\,\,\frac{7}{2} = 3.5 m.\] Area of each of the semi-circle \[=\,\,\,\frac{1}{2}\pi \,\,\times \,\,{{\left( 3.5 \right)}^{2}}\] \[=\,\,\frac{1}{2}\times \frac{22}{7}\times  3.5\times 3.5= 19.25{{m}^{2}}\] Area of shaded region \[= \,4 \times  19.25 = 77 {{m}^{2}}.\]