question_answer

The centroid of a\[\Delta ABC\]is G. The area of \[\Delta ABC\] is \[60\text{ }c{{m}^{2}}.\]The area of \[\Delta GBC\] is

A) \[40\,c{{m}^{2}}\]                  

B) \[20\,c{{m}^{2}}\]

C) \[30\,c{{m}^{2}}\]                  

D) \[10\,c{{m}^{2}}\]

Correct Answer: B

Solution :

Area of \[\Delta ABC=60c{{m}^{2}}\]

\[\because \]       \[AG:GE=2:1\]

\[\therefore \] Area of \[\Delta GBC=\frac{1}{3}\times 60\]

\[=20\,c{{m}^{2}}\]