A6. A regular hexagon and an equilateral triangle have the same perimeter.

What is the ratio of the area of the hexagon to the area of the triangle?
A) $2: 3$
B) $1: 1$
C) $4: 3$
D) $3: 2$
E) $2: 1$
A6. D) $3: 2$ We divide the hexagon into six equilateral triangles and the triangle into four equilateral triangles as shown in the figure. Since the hexagon and the triangle have equal perimeters, the sides of the triangle are twice as long as those of the hexagon. The triangles in these divisions

![](https://cdn.mathpix.com/cropped/2024_04_17_88e9b1bd823632ad9c59g-2.jpg?height=182&width=211&top_left_y=203&top_left_x=1522)
are therefore the same size. The ratio of the areas is therefore $6: 4$, or $3: 2$.