Question

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

Answer 1

Answer:

1:2

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

$\begin{gathered} \frac{A1}{A2}=\frac{3\sqrt[\square]{3}}{2}a^2\text{ }\times\frac{1}{3\sqrt[\square]{3}a^2} \\ \frac{A1}{A2\text{ }}=\frac{1}{2} \end{gathered}$

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