A) \[56c{{m}^{2}}\]
B) \[54c{{m}^{2}}\]
C) \[60c{{m}^{2}}\]
D) \[72c{{m}^{2}}\]
Correct Answer: B
Solution :
[b] In \[\Delta AFC,\] \[AF||HE\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\Delta AFC\tilde{\ }\Delta EHC\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\frac{AF}{HE}=\frac{FC}{HC}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\frac{24}{6}=\frac{6}{HC}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,HC=3/2\,\,cm\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,FH=6-3/2=9/2\,cm\] |
Similarly, \[GF=9/2\] |
\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,GH=\frac{9}{2}+\frac{9}{2}=9\,cm\] |
Area of rectangle \[GHED=GH\times HE\] |
\[=9\times 6=54\,\,c{{m}^{2}}\] |
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