Area Comparison of Triangle and Hexagon

Consider a regular hexagon with a side length of $s$. The hexagon can be divided into six equilateral triangles, each with a side length of $s$. A line is drawn from one vertex of the hexagon to the opposite vertex through the center of the hexagon.

Calculate the area of the triangle formed by this line and two consecutive vertices of the hexagon.

What is the relationship between the area of this triangle (Quantity A) and the area of the entire hexagon (Quantity B)?

Recall that the area of a regular hexagon can be calculated using the formula:

$$ ext{Area}_{ ext{hexagon}} = rac{3 oot{3}}{2}s^2$$

And the area of the triangle can be computed using the formula:

$$ ext{Area}_{ ext{triangle}} = rac{1}{2} imes ext{base} imes ext{height}$$