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

The Correct Option is D

Looking at the figure below:

Upon visual inspection, we observe that:

• The large equilateral triangle can be divided into 9 smaller equilateral triangles of equal area.
• Among them, a regular hexagon is formed by combining 6 of these smaller triangles.

Therefore, the ratio of the area of the hexagon to the area of the triangle is:

\[\frac{\text{Area of Hexagon}}{\text{Area of Triangle}} = \frac{6}{9} = \frac{2}{3}\]

Final Answer: \(\boxed{\frac{2}{3}}\)