Question

abd is a parallelogram with area 80 sq cm. the diagonals ac and bd intersect at o . p is the midpoint of oa calculate ar (bop)

Answer 1

area of parellalogram abcd = 80sq cm.
we know diagonal of parellaogram divides it 2 traingle of equal area so area of abd = dbc = 40 sq cm. bd is the diagonal & ac is the diagonal & we know diagonala bisect each other so area of aod = boa = 40÷2 i.e. 20 sq. cm. p is the mid point of oa it means bp is the median of abo & we know median divides triangle in 2 of equal area so bop = abp = 10 sq cm.
hence bop = 10 sq cm..

Answer 2

area of parellalogram ABCD = 80sq cm.

we know diagonal of parellaogram divides it 2 traingle of equal area so area of [ABD] = [DBC] = 40 sq cm. BD & AC are the diagonals & we know diagonals bisect each other. So, area of [aod] = [boa] = 40÷2 i.e. 20 sq. cm. p is the mid point of OA it means BP is the median of [ABO] & we know median divides triangle in 2 of equal area so, ar[Bop] = ar[abp] = 10 sq cm.

Hence, ar[Bop] = 10 sq cm.