Exercise 19 Page 214

In order to find the area of the athletic field we need to know its width and length. Let's name the points on the given graph and note the rectangle's length and width.

Calculate the Length

From the diagram, we can see that the points A and B are the endpoints of the horizontal segment AB, and their y-coordinates are the same. Using the Ruler Postulate, we can find the length of AB by calculating the difference between the x-coordinates of the endpoints A and B. AB=|x_2-x_1|Let's substitute 10 for x_1 and 110 for x_2, and calculate AB.

AB=|x_2-x_1|

SubstituteII

x_1= 10, x_2= 110

AB=| 110- 10|

SubTerms

Subtract terms

AB=|100|

AbsPos

|100|=100

AB=100

The length of the athletic field is 100 yards.

Calculate the Width

Similarly, we can calculate the width of the field. In this case, the points A and D are the endpoints of the vertical segment and their x-coordinates are the same. Again, using the Ruler Postulate we can find the length of the segment AD by calculating the difference between the y-coordinates of A and D. AD=|y_2-y_1| Let's substitute y_1 with 20 and y_2 with 80, and calculate AD.

AD=|y_2-y_1|

SubstituteII

y_1= 20, y_2= 80

AD=| 80- 20|

SubTerms

Subtract terms

AD=|60|

AbsPos

|60|=60

AD=60

The width of the field is 60 yards.

Calculate the Area

Now that we know both the length and the width of the field, we can calculate its area. Since it has the shape of a rectangle, let's use the formula for a rectangle's area. A=lw If we substitute 100 for l and 60 for w, we will be able to calculate the area A of the field.

A=lw

SubstituteII

l= 100, w= 60

A= 100( 60)

Multiply

Multiply

A=6000

The area of the athletic field is 6000 square yards.