CAT 2019 Question Paper | Quants Slot 1

CAT Questions

Another Geometry question that has appeared in CAT 2019 paper. This is a tough CAT question from the topic of geometry. It involves the concept of construction as well as conversion of one polygon into the other. In our experience, this question again test the fundamentals that has been a consistent theme across all the CAT previous year paper. Try cracking this question though it maybe a good idea to skip this in real life. As always, Geometry forms a major chunk of the CAT syllabus so ensure you spend adequate time on Geometry in your CAT online preparation schedule.

Question 7 : 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. 5 : 6
2. 3 : 4
3. 2 : 3
4. 4 : 5

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Video Explanation

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Explanatory Answer

Construct an Equilateral triangle and cut of equal lengths from all three sides. So we obtain a hexagon and three equilateral triangles of side 'a' in return.
We know that a hexagon comprises of 6 Equilateral Triangles. Since the side of the hexagon is also 'a', we obtain 6 equilateral triangles in return.
Thus, we have a total of 6 + 3 = 9 equilateral triangles of side 'a'
Ratio of area of Hexagon with Area of Triangle = 6: 9 = 2: 3

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The question is "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"

Hence, the answer is 2 : 3

Choice C is the correct answer.