Answer
The area of the field is $6000$ square yards.
Work Step by Step
To find the area of the field, we need to know the dimensions of the field and plug them into the following formula to calculate area:
$A = lw$
To find the dimensions of the rectangle, we use the distance formula to find the length and the width. Then, we can put these dimensions into the formula to calculate area.
The distance between two points is calculated using the following formula:
$D = \sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Let's plug in the coordinates for the length into this formula:
$length = \sqrt {(110 - 10)^2 + (80 - 80)^2}$
Evaluate what's in parentheses first:
$length = \sqrt {(100)^2 + (0)^2}$
Evaluate exponents:
$length = \sqrt {10000}$
Take the square root to solve for $D$:
$length = 100$ yards
Now, let's plug in the coordinates of the width into the distance formula:
$width = \sqrt {(10 - 10)^2 + (80 - 20)^2}$
Evaluate what's in parentheses first:
$width = \sqrt {(0)^2 + (60)^2}$
Evaluate exponents:
$width = \sqrt {3600}$
Take the square root to solve for $D$:
$width = 60$ yards
Now that we have the measurements for the length and width, let's plug the values into the equation to calculate area:
$A = (100)(60)$
$A = 6000$ square yards
The area of the field is $6000$ square yards.
