Trapezium with AB ∥ CD and AB = 2CD – Diagonals intersect at O: Find the ratio of areas [∆AOB] : [∆COD].
Aptitude
Area
Difficulty: Medium
Choose an option
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A4:1
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B1:16
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C1:4
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D16:1
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ENone of these
Answer
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