Question

In the given figure AD is median of $\Delta ABC$, DE is median of $\Delta ABD$ and EF is median of $\Delta BED$. If area of $\Delta ABC$ is $128c{m}^2$, then area of $\Delta BEF$ is

• A. $8c{m}^2$
• B. $16c{m}^2$
• C. $32c{m}^2$
• D. $64c{m}^2$

Answer 1

The correct option is B

$16c{m}^2$

Area $\Delta BEF$ $=\frac{1}{2}\text{area}\Delta BED=\frac{1}{2}\left[\frac{1}{2}\text{area}\Delta BAD\right]=\frac{1}{4}\text{area}\Delta BAD=\frac{1}{2}\left[\frac{1}{4}\text{area}\Delta BAC\right]=\frac{1}{8}\text{area}\Delta BAC=\frac{1}{8}\times 128=16c{m}^2$

Hence (B)