# Area of irregular similar hexagons [closed]

Irregular Hexagons $$A$$ and $$B$$ are geometrically similar. The shortest sides are $$4$$ inches and $$3$$ inches, respectively. If the area of hexagon $$A$$ is $$48in^2$$, what is the area of hexagon $$B$$?

I know the answer is $$27 in^2$$, but how do you get that?

## closed as off-topic by Saad, Leucippus, Xander Henderson, Chris Custer, Ahmad BazziOct 1 '18 at 5:44

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## 2 Answers

Because if corresponding linear dimensions of $$A$$ and $$B$$ are in $$4:3$$ ratio, then their areas are in $$4^2:3^2$$ ratio.

The areas of similar figures vary in proportion to the square of the proportion by which the lengths are stretched. For example, a square with one and one half times the side length has area $$(3/2)^2$$ as large.

Can you answer your question now?