CAT 2025 Geometry & Mensuration Question (Hard)

Question

Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is

Accepted Answer

Let the side of the hexagon be a. The area of the whole hexagon is going to be a 2 2 ! image https optima-learn.b-cdn.net cat-pyq 2025 5ef1a4611d7788e8.png We know that the longest diagonal of a hexagon is 2 times the side of the hexagon. PQ 2 2 1.5a The area of the trapezium Average of parllel side

CAT 2025

Quantitative

Geometry & Mensuration

Hard

$Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is$

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