A) 58
B) 60
C) 61
D) 62
E) 63
Correct Answer: E
Solution :
Let \[({{x}_{1}},{{y}_{1}})=(0,0)\] \[({{x}_{2}},{{y}_{2}})=(12,0)\] \[({{x}_{3}},{{y}_{3}})=(12,2)\] \[({{x}_{4}},{{y}_{4}})=(6,7)\] \[({{x}_{5}},{{y}_{5}})=(0,5)\] \[\therefore \]Area of pentagon \[=\frac{1}{2}\left[ \begin{matrix} {{x}_{1}}{{y}_{2}}+{{x}_{2}}{{y}_{3}}+{{x}_{3}}{{y}_{4}}+{{x}_{4}}{{y}_{5}} \\ +{{x}_{5}}{{y}_{1}}-({{y}_{1}}{{x}_{2}}+{{y}_{2}}{{x}_{3}}+{{y}_{3}}{{x}_{4}}) \\ +{{y}_{4}}{{x}_{5}}+{{y}_{5}}{{x}_{1}}) \\ \end{matrix} \right]\] \[=\frac{1}{2}\left[ \begin{align} & 0(0)+12(2)+12(7)+6(5)+0(0) \\ & -\{0+0+2(6)+7(0)+5(0)\} \\ \end{align} \right]\] \[=\frac{1}{2}[(24+84+30-12)]=63\,sq\,unit\]
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