Question

If two similar hexagons have a similarity ratio of 1:2, then describe the ratio of their areas

Answer 1

1:2

Step-by-step explanation

Let the area of the hexagons be A1 and A2

area of a hexagon is expressed as;

`\text{A1 = }\frac{3\sqrt[\square]{3}}{2}a^2`

Since they are in the ratio of 1:2

A2 = 2A1

`A2\text{ = 2(}\frac{3\sqrt[\square]{3}}{2})a^2`

Take the ratio of their areas

`\begin{gathered} (A1)/(A2)=\frac{3\sqrt[\square]{3}}{2}a^2\text{ }*\frac{1}{3\sqrt[\square]{3}a^2} \\ \frac{A1}{A2\text{ }}=(1)/(2) \end{gathered}`

Hence the ratio of their areas will also be 1:2