Formula: Dodecahedron Area Side length
$$A ~=~ 3 \, a^2 \, \sqrt{25 ~+~ 10 \, \sqrt{5}}$$
$$A ~=~ 3 \, a^2 \, \sqrt{25 ~+~ 10 \, \sqrt{5}}$$
$$a ~=~ \sqrt{ \frac{A}{3\sqrt{25 ~+~ 10 \, \sqrt{5}}} }$$
Area
$$ A $$ Unit $$ \mathrm{m}^2 $$
Area of a dodecahedron. It consists of twelve pentagonal planes. The prefactor is approximately:
$$ 3 \sqrt{25 ~+~ 10 \, \sqrt{5}} \approx 20.646 $$
Side length
$$ a $$ Unit $$ \mathrm{m} $$
Side length of a dodecahedron. Since it is a regular polyhedron, all sides have the same length.