Question

ABCD is a trapezium in which AB is parallel tp DC and AB=2DC,if the diagonals of the diagonals of the trapezium intersect each other at a point 0.Find the ratio of the area of the triangle AOB and triangle COD​

Answer 1

Given, AAB=2CD ....(1)
In △s AOB and COD
∠AOB=∠COD (vert. opp. ∠s)
∠OAB=∠DCO (DC∥AB, alt. ∠s are equal)
∴ △AOB∼△COD (AA similarity)
⇒
ar(△COD)
ar(△AOB)
​
=
CD
2

AB
2

​
{Ratio of areas of two similar △s is equal to the ratio of the squares of the corresponding sides}
=
CD
2

(2CD)
2

​
=
CD
2

4CD
2

​
=
1
4
​
. ....From (1)