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quadrilateral problem

Asked by ashwinivg 20th March 2009, 7:45 AM
Answered by Expert

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


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

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


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


area triangleDEC=1/2(EC*DM)

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


 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.

Answered by Expert 20th March 2009, 8:46 AM
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