Exercise 3 Page 408

To determine the perimeter of the polygon, we must find the sum of its side lengths. This polygon has three vertices, so it is a triangle. 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 DE.

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

SubstitutePoints

Substitute ( - 3,2) & ( 4,2)

DE=sqrt(( 4-( - 3))^2+( 2- 2)^2)

SubNeg

a-(- b)=a+b

DE=sqrt((4+3)^2+(2-2)^2)

AddSubTerms

Add and subtract terms

DE=sqrt(7^2+0^2)

CalcPow

Calculate power

DE=sqrt(49)

CalcRoot

Calculate root

DE=7

We continue by calculating the length of the other two sides EF and FD.

Side	Coordinates	sqrt((x_2-x_1)^2+(y_2-y_1)^2)	Length
EF	( 4,2) ( 4,- 3)	sqrt(( 4- 4)^2+( - 3- 2)^2)	5
FD	( 4,- 3) ( - 3,2)	sqrt(( - 3- 4)^2+( 2-( - 3))^2)	sqrt(74)

Now, let's calculate the perimeter of the triangle. We do so by adding the three sides.

P=DE+EF+FD

SubstituteValues

Substitute values

P=7+5+sqrt(74)

UseCalc

Use a calculator

P= 20.60232...

RoundDec

Round to 2 decimal place(s)

P≈ 20.60

The perimeter of the triangle is approximately 20.60 units.