Question

How would I find the are of the smaller hexagon?

Answer 1

If two hexagons are similar, then their areas are related by:

`(A_1)/(A_2)=k^2...(1)`

Where k is a constant of proportionality. From the problem, we identify:

`\begin{gathered} k=(12)/(8)=(3)/(2) \\ \\ A_1=60\text{ units}^2 \end{gathered}`

Finally, using (1), we can find the area of the smaller hexagon:

`\begin{gathered} (60)/(A_2)=((3)/(2))^2 \\ \\ (A_2)/(60)=(4)/(9) \\ \\ \therefore A_2=(80)/(3)\text{ units}^2 \end{gathered}`