CAT 2019 Geometry & Mensuration Question (Hard)

Question

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

Accepted Answer

Step 1 Let the side length of the equilateral triangle be . Area of an equilateral triangle is given by Step 2 When corners are cut off from triangle , a regular hexagon is formed by slicing off three small equilateral triangles one from each corner . Each removed triangle is also equilateral, and a

CAT 2019

Quantitative

Geometry & Mensuration

Hard

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

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