question_answer

A playground is in the form of a rectangle having semicircle on the shorter sides. Find its area when the length of the rectangular portion is 80 m and the breadth is 42 m.      

A)  \[4746\,{{m}^{2}}\]        

B)  \[77{{m}^{2}}\]

C)  \[1232c{{m}^{3}}\]                       

D)  \[1254c{{m}^{2}}\]

Correct Answer: A

Solution :

Radius of each of semi-circle \[AC=\sqrt{{{a}^{2}}+{{b}^{2}}}=\sqrt{2{{a}^{2}}}=a\sqrt{2}=\sqrt{2}\times \] The required area = 2\[\times \]area of semi-circle EFA + area of rectangle ABDE \[\Delta ABD\] \[\Delta BCD\]