A) \[\frac{49}{4}(\pi -2)\]
B) \[\frac{49}{4}(\pi -1)\]
C) \[\frac{49}{4}(\pi -3)\]
D) \[\frac{49}{2}(\pi -2)\]
Correct Answer: A
Solution :
(a): (Refer to Q. 10: Area (QMS) \[=\frac{1}{2}\times \] standardized area as given is question 10). Area of shaded region = Area of the sector PQMS ? Area of triangle PQS \[QS=\sqrt{2}\] (side) \[=7\sqrt{2}\text{ }cm\] Side = 7cm Area of sector PQS\[=\frac{90{}^\circ }{360{}^\circ }\pi {{(7)}^{2}}=\frac{49\pi }{4}c{{m}^{2}}\] Area of triangle \[PQS=\frac{1}{2}\left( PQ \right)\left( PS \right)\] \[=\frac{1}{2}{{(7)}^{2}}=\frac{49}{2}c{{m}^{2}}\] Required area \[=\left( \frac{49\pi }{4}-\frac{49}{2} \right)c{{m}^{2}}\] \[=\frac{49}{4}(\pi -2)c{{m}^{2}}\]
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