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

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

2 : 3. The given figure can be divided into 9 regions or equilateral triangles of equal areas as shown below, Now the hexagon consists of 6 regions and the triangle consists of 9 regions. Hence the ratio of areas = 6/9 =2:3