In the figure,arcs have been drawn with radii | vedclass

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(A) Given that,the radius of each arc $(r)$ $= 14 \, cm$.The area of a sector with central angle $	heta$ is given by $\frac{	heta}{360^{\circ}} 	im

Vedclass · Accepted Answer

$308$

Vedclass · Answer

(A) Given that,the radius of each arc $(r)$ $= 14 \, cm$.The area of a sector with central angle $	heta$ is given by $\frac{	heta}{360^{\circ}} 	imes \pi r^{2}$.For the three sectors with central angles $\angle P$,$\angle Q$,and $\angle R$,the sum of their areas is:Area $= \frac{\angle P}{360^{\circ}} 	imes \pi r^{2} + \frac{\angle Q}{360^{\circ}} 	imes \pi r^{2} + \frac{\angle R}{360^{\circ}} 	imes \pi r^{2}$Area $= \frac{(\angle P + \angle Q + \angle R)}{360^{\circ}} 	imes \pi r^{2}$Since the sum of the interior angles of a triangle is $180^{\circ}$,we have $\angle P + \angle Q + \angle R = 180^{\circ}$.Area $= \frac{180^{\circ}}{360^{\circ}} 	imes \pi 	imes (14)^{2}$Area $= \frac{1}{2} 	imes \frac{22}{7} 	imes 196$Area $= \frac{1}{2} 	imes 22 	imes 28 = 11 	imes 28 = 308 \, cm^{2}$.Thus,the area of the shaded region is $308 \, cm^{2}$.

In the figure,arcs have been drawn with radii $14 \, cm$ each and with centres $P$,$Q$,and $R$. Find the area of the shaded region (in $cm^{2}$).

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