Exercise 14 Page 57

To find the perimeter and area of the polygon, let's do each step separately.

Calculating the Perimeter

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

The sides of this quadrilateral are vertical lines, and the top and bottom are horizontal lines. This means that these lines are perpendicular to each other, and all of the angles in the polygon are right angles. Therefore, the quadrilateral is a rectangle. We can calculate its perimeter using the following formula. P=2l+2w In this formula, l is the length and w is the width. We can find the measure of the length and width using the Ruler Postulate. Let's start by finding the width using the x-coordinates from YW.

YW=|x_2-x_1|

SubstituteII

x_2= 5, x_1= 2

YW=| 5- 2|

▼

Simplify right-hand side

SubTerm

Subtract term

YW=|3|

AbsPos

|3|=3

YW=3

The width is 3 units. We will now find the length in the same way.

WX=|y_2-y_1|

SubstituteII

y_2= 6, y_1= -1

WX=| 6-( -1)|

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

WX=|6+1|

AddTerms

Add terms

WX=|7|

AbsPos

|7|=7

WX=7

With all of this information, we can calculate the perimeter.

P=2l+2w

SubstituteII

l= 7, w= 3

P=2( 7)+2( 3)

Multiply

Multiply

P=14+6

AddTerms

Add terms

P=20

The rectangle's perimeter is 20units.

Calculating the Area

To calculate the area of rectangle, we can use the following formula. A=l w Similarly, in this formula l is the length and w is the width. As we have already calculated all of these, we have enough information to calculate the area.

A=l w

SubstituteII

l= 7, w= 3

A=( 7)( 3)

Multiply

Multiply

A=21

The rectangle's area is 21square units.