A geometry problem by Ranganath Govardhanam

$\text{The area required is 4 times the green area } CDE. \\D~ is ~midpoint~ of ~CB.~~~DE\parallel BA.\\\therefore~CDE=\dfrac {1}{4} ABC.~~~ABC =\dfrac {1}{4}BigSquare.\\\therefore 4*CDE=4*\dfrac {1}{4} ABC=\dfrac {1}{4}BigSquare.\\ \boxed { \dfrac {1}{4} }$

The shaded square has edge with side length: $\frac{1}{\sqrt{5}}$ Each of three-angles beside of this shaded star is a right three-angles with one side of right angle is equal to: $\frac{1}{2 \times \sqrt{5}}$ The other side with length: $\frac{1}{4 \times \sqrt{5}}$ So it is easy to get area of the shaded star is: $\frac{1}{5} \times ({1+\frac{1}{4}})=\boxed{\frac{1}{4}}$