• # question_answer Semi-circular lawns are attached to the edges of a rectangular field measuring$42\,\,m\times 35\,\,m$. Find the area of the total field. A) $3895.6\,\,{{m}^{2}}$       B)  $3818.5\,\,{{m}^{2}}$C) $3735.6\,\,{{m}^{2}}$                   D)  $3899.9\,\,{{m}^{2}}$

From figure, it is seen that total area of lawn on length face = circle ${{C}_{1}}=\pi {{l}^{2}}/4$ $'l'$ becomes diameter. Similarly, ${{C}_{2}}=\frac{\pi {{b}^{2}}}{4}$ $\therefore$  Total area $=\frac{\pi }{4}\times \left( {{42}^{2}}+{{35}^{2}} \right)$ $=\frac{11\times 7}{2}\left( {{6}^{2}}+{{5}^{2}} \right)\frac{77\times 61}{2}$ To, this we add are of rectangle, ${{A}_{2}}=l\times b$ $=42\times 35=1470\Rightarrow$Total area $=\frac{77\times 61}{2}+1470$