13. The diagram shows a rhombus and two sizes of regular hexagon. What is the ratio of the area of the smaller hexagon to the area of the larger hexagon?
A $1: 2$
B $1: 3$
C $1: 4$
D $1: 8$
E 1:9
13. C Let the length of each edge of the rhombus be $x$. Then, as the rhombus and the smaller regular hexagon have an edge in common, the length of each edge of this hexagon is also $x$. So the length of each edge of the larger regular hexagon is $2 x$. The two regular hexagons are similar. Therefore the ratio of their areas is the square of the ratio of their edge-lengths, that is $1^{2}: 2^{2}=1: 4$.