The apothem of a polygon is given by the formula

where s is the length of side and n is the number of sides of the polygon
Here the side length is 2 meters and number of sides is 6 hence the apothem is given by:
![\begin{gathered} a=(2)/(2)\tan ((360)/(6)) \\ a=\sqrt[]{3}\text{ meters} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/lsknxy8padkw6fm3kzjghvskkay6x74z0s.png)
Hence the apothem is the square root of 3 which is approximately 1.732 meters.