Trapezium with AB ∥ CD and AB = 2CD – Diagonals intersect at O:\nFind the ratio of areas [∆AOB] : [∆COD].

Difficulty: Medium

4:1
1:16
1:4
16:1
None of these

Correct Answer: 4:1

Explanation:

Introduction / Context:
In a trapezium with parallel sides AB and CD, the triangles formed by the diagonals at the ends of the parallel sides are similar; their areas are in the square of the ratio of the parallel sides.

Concept / Approach:
If AB ∥ CD, then [∆AOB] : [∆COD] = (AB/CD)^2.

Step-by-Step Solution:

Given AB = 2CD ⇒ (AB/CD) = 2.Therefore area ratio = 2^2 = 4 : 1.

Final Answer:
4:1

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