Diagonals of a trapezium PQRS intersect each other at at the point 0, PQRS and PQ = 3RS. Find the ratio of the areas of ∆POQ and ∆ROS.


Given,

PQRS is a trapezium in which PQRS and PQ = 3RS




In ∆POQ and ∆ROS,


SOR = QOP [vertically opposite angles]


SRP = RPQ [alternate angles]


∆POQ ∆ROS [by AAA similarity criterion]


By property of area of similar triangle,



[from Equation (i)]



Hence, the required ratio is 9:1.


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