Question

diagonal AC and BD of quadrilateral ABCD intersect at O in such a way that area of a body is equal to area of B O C prove that ABCD is a trapezium

Answer 1

It is given that
Area (DAOD) = area (DBOC)
Area (DAOD) + area (DAOB) = area (DBOC) + area (DAOB)
Area (DADB) = area (DACB)
We know that triangles, on same base having areas equal to each other lie
between the same parallels.
So, these triangles DADB and DACB are lying between the same parallels.
i.e. AB || CD
So, ABCD is a trapezium