Exercise 10 Page 32

When drawing the polygon, the first thing we should notice is its shape. This polygon has four vertices, so it is a quadrilateral. Let's draw it in a coordinate plane.

Notice that the sides of the quadrilateral are vertical lines and that the top and bottom are horizontal lines. Vertical and a horizontal lines are perpendicular to each other. This means that all of the angles in the polygon are right angles and that the quadrilateral is a rectangle. We can calculate its area using the formula for the area of a rectangle. A=l w 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 with KL.

KL=|x_2-x_1|

SubstituteII

x_1= - 3, x_2= 3

KL=| 3-( - 3)|

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

KL=|3+3|

AddTerms

Add terms

KL=|6|

AbsPos

|6|=6

KL=6

The length is 6 units. We will now find the width, LM, in the same way.

LM=|y_2-y_1|

SubstituteII

y_1= 3, y_2= - 1

LM=| - 1- 3|

▼

Simplify right-hand side

SubTerm

Subtract term

LM=|- 4|

AbsNeg

|-4|=4

LM=4

The width is 4 units. We can now calculate the rectangle's area. A=l w ⇒ 6* 4=24 square units