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​

Answer 1

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

Answer

2 : 3