Question

P is a point on AB in parallelogram ABCD, prove ar(ADP)+ ar(BCP)=1/2 ar(ABCD)

Answer 1

in llgm ABCD draw a line through point p join H and F line AB and CD respectively therefore
AHFD is llgm and BHFC is llgm
llgm AHFD and ADP lie on the same base between same ll
at
ar ADP =ar 1/2ar AHFD 1
llgm BHFC and BCP lie on the same base between same ll
at BCP=1/2ar BHFC 2
add 1and 2
ar ADP+ar BPC =1/2ABCD