Question

Show that ar(quad. ABCD)=1/2BD (AM+CM). BD is one of the diagonal of a quadrilateral ABCD , AM and CN are the perpendicular from A and C .

Answer 1

area of quad ABCD=area of triangle ABD +area of triangle BDC

Case I

area of triangle ABD=1/2×b×h
=1/2×BD×AM

case II

area of triangle BDC=1/2×b×h
=1/2×BD×CN

area of quadABCD= 1/2×BD×AM+1/2×BD×CN
1/2×BD(AM+CN)


hence proved

Answer 2

Here is your answer.... ♠️♠️

Area of quadrilateral ABCD =area of triangle ABD +CDB

=1/2×DB×AM + 1/2×DB×CN

=(DB×AM)÷2 + (DB×CN) ÷2

=DB(AM+CN) ÷2

=1/2 BD × (AM+CN)

Hope this helps you...