\(\Delta ABC_{ }\simeq\Delta ADE\)
\(\Rightarrow\frac{S_{\Delta ADE}}{S_{\Delta ABC}}=\left(\frac{AE}{AC}\right)^2\)
\(\Rightarrow\frac{S_{\Delta ADE}}{S_{\Delta ABC}}=\sin^230=\frac{1}{4}\)
\(\Rightarrow S_{\Delta ADE}=\frac{1}{4}\)
\(\Rightarrow S_{BECD}=S_{ABC}-S_{ADE}=1-\frac{1}{4}=\frac{3}{4}\)