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

• A. 5: 6
• B. 4: 5
• C. 3: 4
• D. 2: 3

Answer 1

Answer: (D)

2: 3

Answer 2

Looking at the figure below:

we observe that the triangle can be subdivided into 9 smaller equilateral triangles that intersect at a common point.
Additionally, the hexagon contains 6 of these smaller triangles.
Therefore, the desired ratio is $\frac{6}{9}$, which simplifies to $\frac{2}{3}$.