Answer
$15\sqrt{3}$
Work Step by Step
Adding all the sides of the trapezoid, the perimeter is
\begin{array}{l}\require{cancel}
3\sqrt{3}+2\sqrt{12}+\sqrt{12}+2\sqrt{27}
.\end{array}
Using the properties of radicals, the expression above simplifies to
\begin{array}{l}\require{cancel}
3\sqrt{3}+2\sqrt{4\cdot3}+\sqrt{4\cdot3}+2\sqrt{9\cdot3}
\\\\=
3\sqrt{3}+2\sqrt{(2)^2\cdot3}+\sqrt{(2)^2\cdot3}+2\sqrt{(3)^2\cdot3}
\\\\=
3\sqrt{3}+2(2)\sqrt{3}+2\sqrt{3}+2(3)\sqrt{3}
\\\\=
3\sqrt{3}+4\sqrt{3}+2\sqrt{3}+6\sqrt{3}
\\\\=
15\sqrt{3}
.\end{array}
