quadrilateral problem

Construction: drop perpendiculars from D and B onto AC.Let these perpendiculars be DM and BN respectively..

Now,

 consider are triangle DAE=1/2*(AE*DM)

area triangle BEC=1/2*(EC*BN)

So,

 area DAE*  area BEC=1/4*(AE*DM*EC*BN)...(i)

Simly,

area triangleDEC=1/2(EC*DM)

area triangle AEB=1/2(AE*BN)

So,

 area  DEC*areaAEB=1/4(EC*DM*AE*BN)...(ii)

from (i) and (ii) we get,

the desired result.

Note that the perpendicular(height) for a triangle can be on the extended base as well like in the case of triangles  DEC and AEB.