The correct answer is 39 units.
Parameter is the sum of the lengths of all sides of a polygon. The sides of the polygon are PT, TS, SR, RQ, and QP. To get the length of a side, we use the distance formula:
d =\(\sqrt{ (x_{2} - x_{1}) ^{2} + ( y_2 - y_1)^2}\)
Each vertex in the polygon has its corresponding points:
P (-2,11)
T (8, 7)
S (1, 7)
R (2, 0)
Q (-4,5)
So to get the length of side PT, we use the distance formula and the vertices of side PT:
P \((x_{1} , y_1)\) = (-2, 11)
T \(( x_{2} , y_2)\) = (8, 7)
\(d = \sqrt{ (x_{2} - x_{1}) ^{2} + ( y_2 - y_1)^2}
d = \sqrt{ ({8} - {(-2)}) ^{2} + ( 7 - 11)^2}
d = \sqrt{116}\)
The length of PT is \(\sqrt{116}\)
The same procedure is done for the other 4 sides and the following are the answers:
TS = \(\sqrt{49}\)
SR = \(\sqrt{50}\)
RQ = \(\sqrt{61}\)
QP = \(\sqrt{40}\)
And by adding all the sides, you get the perimeter:
\(\sqrt{116} + \sqrt{49} + \sqrt{50} + \sqrt{61} + \sqrt{40} = 38.97\)
By rounding off, the answer is 39 units.
