Exercise 13 Page 410

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, MN=2 units. Let's now use the Distance Formula to find NP.

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

SubstitutePoints

Substitute ( - 1,- 2) & ( 2,0)

NP = sqrt(( - 1- 2)^2 + ( - 2- 0)^2)

SubTerms

Subtract terms

NP=sqrt((- 3)^2+(- 2)^2)

CalcPow

Calculate power

NP=sqrt(9+4)

AddTerms

Add terms

NP=sqrt(13)

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.

P=NP + PL + LM + MN

SubstituteValues

Substitute values

P= sqrt(13)+sqrt(40)+5+2

UseCalc

Use a calculator

P = 16.93010...

RoundDec

Round to 2 decimal place(s)

P ≈ 16.93

We have now found that the polygon's perimeter is approximately 16.93 units.