The approximate length of string lights the staff needs to decorate the ceiling is 40.25
The complete question is added as an attachment
From the attached figure, we have the following coordinates
A = (5, 16)
B = (17, 10)
C = (14, 4)
D = (2, 10)
Calculate the lengths AB and BC using the following distance formula
d = √[(x2 - x1)^2 + (y2 - y1)^2]
This gives
AB = √[(5- 17)^2 + (16- 10)^2] = 13.4
BC = √[(14- 17)^2 + (4- 10)^2] = 6.7
The approximate length of string lights the staff needs to decorate the ceiling is then calculated as
P = 2 * (AB + BC)
This gives
P = 2 * (13.4 + 6.7)
Evaluate
P = 40.2
Hence, the approximate length of string lights the staff needs to decorate the ceiling is 40.25
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