Diagonals of a trapezium PQRS intersect each other at the point O

• Geometry (C10)

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

Answer

In ∆POQ and ∆ROS

∠P = ∠R

∠Q = ∠S

∴ ∆POQ ~ ∆ROS (AA similarity)

ar (∆POQ) / ar (∆ROS) = (PQ/RS)²

= (3/1)²

= 9/1

∴ ar(∆POQ) : ar(∆ROS) = 9 : 1