Geometry

The sides of a 30-60-90 triangle is in the ratio $1: \sqrt{3} : 2$.

The hypotenuse is 11, so the sides are of lengths $\frac{11}{2}$ and $\frac{11\sqrt{3}}{2}$.

The perimeter is $\frac{11}{2} + \frac{11\sqrt{3}}{2} + 11 \approx \boxed{26.02}$