6. The equilateral triangle and regular hexagon shown have perimeters of the same length.
What is the ratio of the area of the triangle to the area of the hexagon?

A $5: 6$
B $4: 5$
C $3: 4$
D $2: 3$
E $1: 1$
6. D Let the length of the side of the regular hexagon be $a$.
Then its perimeter is $6 a$. Therefore the perimeter of the equilateral triangle is also $6 a$, so the length of each of its
sides is $2 a$. The diagrams show that the equilateral triangle may be divided up into 4 equilateral triangles of side $a$, whereas the regular hexagon may be divided into 6 such triangles. So the required ratio is $4: 6=2: 3$.