Corners are cut off from an equilateral triangle - Quantitative Aptitude – Geometry | Mensuration |

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The question below is from previous year CAT question from CAT 2019 exam comes from CAT Geometry– Mensuration– Corners are cut off from an equilateral triangle …

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2019 – Slot 1 - CAT Mensuration - Question 5 - Corners are cut off from an equilateral triangle

Q. 5: 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

Show Answer

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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