Join \(B\) and \(D\) to form line segment \(\overline{BD}\). Since \(BD\) is diagonal, length of \(BD = \sqrt{2}\)

Now extend line segment \(\overline{CE}\) downwards perpendicular to line segment \(\overline{BD}\) and let its point of intersection be \(F\)

By observation, \(Ar(BCE) = Ar(DCE)\) and \(Ar(BCE) + Ar(DCE) = Ar(BCDE) \Rightarrow Ar(BCDE) = 2Ar(BCE)\)

Now again by observation,

\(Ar(BCDE) = 2Ar(BCE) = Ar(BED) - Ar(BCD) = \frac{1}{2}*EF*BD - \frac{1}{2}*CF*BD = \frac{1}{2}*(EF-CF)*BD\)

\(2Ar(BCE) = \frac{1}{2}*(EF-CF)*BD \Rightarrow Ar(BCE) = \frac{1}{4}*(EF-CF)*BD\)

\(Ar(BCE) = \frac{1}{4}*(EF-CF)*BD = \frac{1}{4}*([CE + CF]-CF)*BD = \frac{1}{4}*(CE)*BD\)

\(Ar(BCE) = \frac{1}{4}*(1)*\sqrt{2} = \frac{\sqrt{2}}{4}\)

Hence, Answer is B