Mensuration Practice Test 5

Perimeter of the square = Perimeter of the regular hexagon.
Side of the square = $\frac{\mathit{P}}{4}$
Side of the hexagon = $\frac{\mathit{P}}{6}$
Ratio of area of hexagon to the area of square
$\frac{3\sqrt{3}}{4}\times {\left(\frac{\mathit{P}}{6}\right)}^2:{\left(\frac{\mathit{P}}{4}\right)}^2$
$\frac{3\sqrt{3}}{4}\times \frac{{\mathit{P}}^2}{36}:\frac{{\mathit{P}}^2}{16}$
$\frac{\sqrt{3}}{3^2}:1$
$\sqrt{3}:3$
1 : $\sqrt{3}$