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GATE 2021 EC – Question 10

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

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

Diagram for GATE 2021 EC question 10
  1. 2 : 3
  2. 3 : 4
  3. 4 : 5
  4. 5 : 6

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Show answer and explanation

Correct answer: (A) 2 : 3

Explanation

For the cut-off pieces to leave a regular hexagon, each corner removed is an equilateral triangle of side $\frac13$ of the original side. Its area is $\frac19$ of the original, so the three corners remove $\frac39=\frac13$. The hexagon is $\frac23$ of the triangle, a ratio of $2:3$.