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 $\Delta BEF$ is $4c{m}^2$, then area of $\Delta ABC$ is

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

Answer 1

The correct option is C

$32c{m}^2$

We know that median divides a triangle into two triangles of equal area.

Area $\Delta BED$ $=2\text{area}\Delta BEF=2\left(4\right)=8c{m}^2$

Area $\Delta BAD$$=2\text{area}\Delta BED=2\left(8\right)=16c{m}^2$

Area $\Delta ABC$$=2\text{area}\Delta BAD=2\left(16\right)=32c{m}^2$

Hence (C)