Question

Given a $△ABF$ in which $BE=EF,BD=DE$ and $BC=CD$. Area of $△ABF=64$ sq. units.

Find the area of $△ABC$

• A. $32$ sq. units
• B. $16$ sq. units
• C. $10$ sq. units
• D. $8$ sq. units

Answer 1

The correct option is D

$8$ sq. units

Since, $BE=EF$, so, $AE$ is the median of $△ABF$ and it divides it into two triangles of equal area.

$\Rightarrow$ Area of $△ABE=\frac{\text{area of triangle ABF}}{2}=\frac{64}{2}=32$ sq. units

Now, $BD=DE$, so, $AD$ is the median of $△ABE$ and it divides it into two triangles of equal area.

$\Rightarrow$ Area of $△ABD=\frac{\text{area of triangle ABE}}{2}=\frac{32}{2}=16$ sq. units

Now, $BC=CD$, so, $AC$ is the median of $△ABD$ and it divides it into two triangles of equal area.

$\Rightarrow$ Area of $△ABC=\frac{\text{area of triangle ABD}}{2}=\frac{16}{2}=8$ sq. units