Exercise 7 Page 409

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 MN.

MN=|x_2-x_1|

SubstituteII

x_2= 6, x_1= 2

MN=| 6- 2|

SubTerm

Subtract term

MN=|4|

AbsPos

|4|=4

MN=4

The length l is 4 feet. We will find the width in the same way.

MR=|y_2-y_1|

SubstituteII

y_2= - 3, y_1= 2

MR=| - 3- 2|

SubTerm

Subtract term

MR=|- 5|

AbsNeg

|-5|=5

MR=5

Therefore, w=5 feet. We can now calculate the area. A=l w ⇒ 4* 5=20 square feet