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 =[tex] \sqrt{ (x_{2} - x_{1}) ^{2} + ( y_2 - y_1)^2} [/tex]
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 [tex] (x_{1} , y_1)[/tex] = (-2, 11)
T [tex]( x_{2} , y_2)[/tex] = (8, 7)
[tex]d = \sqrt{ (x_{2} - x_{1}) ^{2} + ( y_2 - y_1)^2}
d = \sqrt{ ({8} - {(-2)}) ^{2} + ( 7 - 11)^2}
d = \sqrt{116} [/tex]
The length of PT is [tex] \sqrt{116} [/tex]
The same procedure is done for the other 4 sides and the following are the answers:
TS = [tex] \sqrt{49} [/tex]
SR = [tex] \sqrt{50} [/tex]
RQ = [tex] \sqrt{61} [/tex]
QP = [tex] \sqrt{40} [/tex]
And by adding all the sides, you get the perimeter:
[tex] \sqrt{116} + \sqrt{49} + \sqrt{50} + \sqrt{61} + \sqrt{40} = 38.97[/tex]
By rounding off, the answer is 39 units.
