Question

Medians of $△ABC,$ intersect at G. If $ar\left(△ABC\right)=27c{m}^2$ then $ar\left(△BGC\right)=$

• A. $6c{m}^2$
  
• B. $9c{m}^2$
  
• C. $12c{m}^2$
  
• D. $18c{m}^2$
  

Answer 1

The correct option is B

$9c{m}^2$

In $△ABC,AD,BE$ and CF are the medians Which intersect each other at G

Area of $△ABC=27c{m}^2$
$\because ar\left(△GBC\right)=ar\left(△GCA\right)=ar\left(△GAB\right)=\frac{1}{3}ar\left(△ABC\right)=\frac{1}{3}\times 27c{m}^2=9c{m}^2$