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)  \[4748\,{{m}^{2}}\]

C)  \[4950\,{{m}^{2}}\]           

D)  \[5049\,{{m}^{2}}\]

Correct Answer: A

Solution :

    Radius of each of semi-circle \[=\frac{42}{2}=21\,m\] The required area = 2\[\times \]area of semi-circle EFA + area of rectangle ABDE \[=2\times \frac{1}{2}\pi {{(21)}^{2}}+80\times 42\] \[=\frac{22}{7}\times 21\times 21+80\times 42=4746\,{{m}^{2}}.\]