Quantitative Aptitude – Geometry – Mensuration

Slot – 1 – Quantitative Aptitude – Geometry – Mensuration – Corners are cut off from an equilateral triangle

Q. Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is?

1. 3 : 4
2. 2 : 3
3. 5 : 6
4. 4 : 5

Answer: 2 : 3

Solution: In given case , figure can be drawn as below

Let side of equilateral triangle ABC = 3a
So side of hexagon = a
Area of triangle = (root3 /4 )*(3a)^2 = 9a^2 *(root3/4)
Area of hexagon with side a = 6*(root3 /4 )*(a)^2
Ratio of areas of hexagon to that of triangle = { 6*(root3 /4 )*(a)^2 } / { 9a^2 *(root3/4)} = 6/9 = 2/3
Thus required ratio = 2 : 3

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