Question

ABCD is a trapezium in which AB is parallel to DC and 2AB=3DC. Find the ratio of areas of triangle AOB and triangle COD. please help me.

Answer 1

Thank you for asking this question. Here is your answer:

Angle DOC = BOA (vertically opposite angles are equal)

Angle CDO = ABO (alternate interior angle)

Angle DCO = BAO  

So, triangle AOB and Cod are similar

We will use the similarity rule here,  

(area of triangle AOB)/(area of triangle COD) =(AB/CD)^2

=(2CD/CD)^2=4

=4:1

If there is any confusion please leave a comment below.