The polygon has four sides, NP, PL, LM, and MN. We can find the perimeter by adding the polygon's side lengths. First, we must find the length of each side. Since MN is a horizontal line, we can find its length using the Ruler Postulate. For the other sides, we will use the
Distance Formula. Let's begin with MN.
Thus, NP=sqrt(13) units. We will find PL and LM in the same way.
Side
Coordinates
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Length
PL
(- 1, - 2) (1,4)
sqrt(( 1-( - 1))^2+( 4-( - 2))^2)
sqrt(40)
LM
(1,4) (4,0)
sqrt(( 4- 1)^2+( 0- 4)^2)
5
To recall, we have the following lengths in units.
MN:& 2
NP:& sqrt(13)
PL:& sqrt(40)
LM:& 5
We can now calculate the perimeter which is the sum of the length of the sides.
