The trapezoid is isosceles. Thus, the bases are [tex]\overline{KL}[/tex] and [tex]\overline{NM}[/tex], while the equal sides are [tex]\overline{LM}[/tex] and [tex]\overline{KN}[/tex].
This also means that the length of the sides [tex]\overline{LM}[/tex] and [tex]\overline{KN}[/tex] are equal.
The perimeter of the trapezoid is the sum of the lengths of the sides of the trapezoid, so the perimeter is:
[tex]KL+LM+MN+NL=2 \sqrt{2}+ \sqrt{5}+ \sqrt{2}+\sqrt{5}=3 \sqrt{2}+2 \sqrt{5}. [/tex]
Answer: third choice
