Question

BD is one of the diagonals of a quadrilateral ABCD . AM and CN are the perpendicular from A and
C respectively on BD show that ar (ABCD)=0.5 BD (AM+CN)

Answer 1

draw the figure by yourself.

we know that,
area of ∆= 1/2×base×height

ar of ∆ADB =1/2×BD×AM -------------1
ar of ∆CDB =1/2×BD×CN-------------2
Ar of quad. ABCD = Ar of ∆ADB+Ar of ∆CDB
= 1/2×BD×AM+ 1/2×BD×CN
=1/2×BD×(AM+ CN)
HENCE PROVED