GATE 2021 ES – Question 10

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Corners are cut from an equilateral triangle to produce the shown regular convex hexagon. Find hexagon area/original triangle area.

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Correct answer: (A) 2:3

Explanation

Let each regular hexagon side be a. Each removed corner is an equilateral triangle of side a, and the original triangle has side 3a. Areas scale as side squared, so each removed triangle has 1/9 of original area. Retained fraction = 1−3/9 = **2/3, A**.

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