Exercise 16 Page 64

To determine the perimeter of the polygon, we must find the sum of its side lengths. This polygon has four vertices, so it is a quadrilateral. Let's draw it in a coordinate plane.

Before we can find the sum of the side lengths, we must find the length of each side. We can use the Distance Formula to do this. Let's start with LM.

LM = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)

SubstitutePoints

Substitute ( 3,5) & ( 0,1)

LM = sqrt(( 3- 0)^2 + ( 5- 1)^2)

SubTerms

Subtract terms

LM=sqrt(3^2+4^2)

CalcPow

Calculate power

LM=sqrt(9+16)

AddTerms

Add terms

LM=sqrt(25)

CalcRoot

Calculate root

LM=5

We continue by calculating the length of the other three sides MN, NP, and PL.

Side	Coordinates	sqrt((x_2-x_1)^2+(y_2-y_1)^2)	Length
MN	( 3,5) ( 5,5)	sqrt(( 5- 3)^2+( 5- 5)^2)	2
NP	( 5,5) ( 5,1)	sqrt(( 5- 5)^2+( 1- 5)^2)	4
PL	( 5,1) ( 0,1)	sqrt(( 0- 5)^2+( 1- 1)^2)	5

Now, let's calculate the quadrilateral's perimeter. We do so by adding the four sides.

P=LM+MN+NP+PL

SubstituteValues

Substitute values

P=5+2+4+5

AddTerms

Add terms

P=16

The quadrilateral's perimeter is 16 units.