Exercise 14 Page 410

The given polygon has six sides, AB, BC, CD, DE, EF, and FA. Four of these sides are either vertical or horizontal, so for these cases we can use the Ruler Postulate. Let's start with BC. We can do all four vertical and horizontal sides of the polygon in the same way.

Side	Coordinates	|x_2-x_1| or |y_2-y_1|	Length
BC	(2,0) (2,- 2)	|y_2-y_1|→ | - 2- 0|	2
CD	(2,- 2) (0,- 2)	|x_2-x_1|→ | 0- 2|	2
EF	(- 2,2) (- 2,4)	|y_2-y_1|→ | 4- 2|	2
FA	(- 2,4) (0,4)	|x_2-x_1|→ | 0-( - 2)|	2

For the remaining two sides, we will need to use the Distance Formula. Let's start with AB.

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

SubstitutePoints

Substitute ( 2,0) & ( 0,4)

AB = sqrt(( 2- 0)^2 + ( 0- 4)^2)

SubTerms

Subtract terms

AB=sqrt(2^2+(- 4)^2)

CalcPow

Calculate power

AB=sqrt(4+16)

AddTerms

Add terms

AB=sqrt(20)

We will find the length of DE in the same way, giving us both of our remaining side lengths.

Side	Coordinates	sqrt((x_2-x_1)^2+(y_2-y_1)^2)	Length
AB	(0,4) (2,0)	sqrt(( 2- 0)^2+( 0- 4)^2)	sqrt(20)
DE	(0,-2) (-2,2)	sqrt(( -2- 0)^2+( 2-( -2))^2)	sqrt(20)

We can now calculate the perimeter which is the sum of the length of the sides.

P=AB + BC + CD + DE + EF + FA

SubstituteValues

Substitute values

P= sqrt(20) + 2 + 2 + sqrt(20) + 2 + 2

UseCalc

Use a calculator

P = 16.94427...

RoundDec

Round to 2 decimal place(s)

P ≈ 16.94

The polygon's perimeter is P ≈ 16.94 units.