Sides GF and DE are easy to measure. Just count units.
GF = 5
DE = 3
Sides DG and EF need a little calculation.
Think of side DG as the hypotenuse of a right triangle whose legs measure 1 and 2 units. Using the Pythagorean theorem, we can find the lengths of DG and EF.
2^2 + 1^2 = DG^2
4 + 1 = DG^2
5 = DG^2
DG = sqrt(5)
Perimeter = 5 + 3 + sqrt(5) + sqrt(5)
Perimeter = 8 + 2sqrt(5)
Perimeter is approximately 12.5 units