Is there a relation among areas of concentric polygons? Is there a way to calculate the area of concentric, convex polygons? I need a fast way to calculate the area of several, concentric polygons. I have their centroid in Cartesian coordinates and the height of the rings the others form with the sides of the first one ($h_1, h_2, h_3, ..., h_n$). Please, see the picture below for a better understanding.

Although the polygons in the picture are close to regular polygons, they aren't. I have the area of the smallest one, so I would like a way to calculate the others by using a rate based on their heights.
 A: As is mentioned in the comments if the area of the smallest polygon is $A$ then the area of the $i$th one is $A(\dfrac{h_i}{h_1})^2$ where $h_1$ and $h_i$ are the distances from the origin to the first and $i$th polygon along a given direction.
A: The relationship is based on similarity, and is independent of the fact that they're regular polygons. It would work the same even with irregular figures scaled proportionally.
If a particular corresponding linear dimension is compared between the larger and smaller figure, with the ratio being $k$, then the ratio of enclosed areas is $k^2$. Most commonly corresponding sides of polygons are used in the comparison, but there's no need to: any linear dimension can be used as long as you can define a relationship between the corresponding reference points in each figure. So, as in this case, the distance from a common centre (that remains invariant to the scaling transform) to the midpoint of a side is fine.
Here, the ratio of sides $k = \frac {h_2} {h_1}$, so the ratio of areas is $k^2 =  \frac {h_2^2} {h_1^2}$
