GATE EC 2021 Set 1 — Question 10
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is ________
Correct answer
(A) 2: 3
Solution
Let the side of the original equilateral triangle be . An equilateral triangle of side can be divided into smaller equilateral triangles of side . To form a regular hexagon, we cut off an equilateral triangle of side from each of the three corners. The resulting regular hexagon has a side length of . A regular hexagon of side is composed of 6 equilateral triangles of side . Therefore, the ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is . Thus, the ratio is 2 : 3.
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