Question

diagonals AC and BD of a trapezium ABCD with AB II DC intersect each other at O.
prove that ar(AOD) =ar(BOC)

Answer 1

see, as the 2 lines are parallel to each other the 2 triangles ACD and BCD are equal in area so, put it as equation 1.
subtract triangle COD from equation 1.
.
u will get ar(AOD)=ar (BOC)

Answer 2

Here you go!!!

Given that ABCD is a trapezium with AB || DC and Diagonal AC and BD intersect each other at O.

To prove: Area (AOD) = Area (BOC)

Proof: ΔADC and ΔBDC are on the same base DC and between same parallel AB and DC.

∴Area (ΔADC) = Area (ΔBDC) [triangles on the same base and between same parallel are equal in area]

Subtract Area (ΔDOC) from both side

Area (ΔADC) – Area (ΔDOC) = Area (ΔBDC) – Area (ΔDOC)

Area (ΔAOD) = Area (ΔBOC)

Hence proved✅.