Solution :
Since \(\triangle\) ABC and BDE are equilateral triangles, they are equiangular and hence
\(\triangle\) ABC ~ \(\triangle\) BDE
So, \(area(\triangle ABC)\over area(\triangle BDE)\) = \({BC}^2\over {BD}^2\)
orย \(area(\triangle ABC)\over area(\triangle BDE)\) = \({2BD}^2\over {AC}^2\)
\(\implies\)ย \(area(\triangle ABC)\over area(\triangle BDE)\) = \(4\over 1\)
\(\therefore\) (d) is the correct answer.