I think it will be 8 1/3 inches.
(7,7) and (7,3) are 4 units apart
7-3 = 4
7-7 = 0
(7,3) and (10,3) are 3 units away
3-3 = 0; 10-7 = 3
(7,7) and (10,3) are 4/3 units away or 1 and 1/3
7-3 = 4
7-10 =-3
Then, take the absolute value because you can't have negative inches of lace, you get 4/3 or 1 1/3.
Add them all together for perimiter:
4+3+1 1/3 = 8 1/3 inches of lace
Hope this helps!