Can you do it?

$\triangle ABD \text{area}+\triangle ADC \text{area}=1$

As $\triangle ABD$ and $\triangle ADC$ have same height and same base.

$\triangle ABD \text{area}=\triangle ADC \text{area}=\frac{1}{2}$

As $\triangle ABE$ and $\triangle BED$ have same height and same base.

$\triangle ABE \text{area}=\triangle BED \text{area}=\frac{1}{4}$

As $\triangle BED$ and $\triangle DEC$ have same height and same base.

$\triangle BED \text{area}=\triangle DEC \text{area}=\frac{1}{4}$

As $\triangle BCF$ and $\triangle FCE$ have same height and same base.

$\triangle BCF \text{area}=\triangle FCE \text{area}=\frac{1}{4}$

As $\triangle EFG$ and $\triangle EGC$ have same height and same base.

$\triangle EFG \text{area}=\triangle EGC \text{area}=\frac{1}{8}$

$\boxed{\triangle EFG\text{area}=\frac{1}{8}=0.125}$

The median of triangle devides the triangle in two part of equal area....the answer is 0.125