Question

ABCD is a trapezium.Diagonals AC and BD intersects each other at O.Find the ratio of ar( ⚠AOD)=ar (⚠
BOC)

Answer 1

in fig AB//DC
So ar of ADC=ar of BDC (they are on same base DC and they are between same //s)
subtract ar of DOC from both sides , we get
ar of ADC - ar of DOC = ar of BDC - ar of DOC
=> ar of ADO = ar of BOC

Answer 2

Heya!!

Triangle ABD and triangle ABC are on same base AB and between same parallel AB and DC
So ar (ABD)=ar (ABC)
in these two triangles triangle AOB is common. So subtract ar(AOB)
​ar (ABD)-ar (AOB)=ar (ABC)-ar( AOB)
​ar (AOD)=ar(BOC)
​So their ratio will be 1

Hope it helps u :)