Question

Find the area of the polygon defined by the coordinates (0, -5), (-5, 0), (-15, -20), and (-20, -15).

Answer 1

This is a rectangle... Did you draw the points?
 
Find
- the length of the segment going from (-5,0) to (0,-5)
- and the length of the segment from (-20,-15) to (-15,-20).

These are the length and width of the rectangle; multiply both quantities.

The width is found with the formula:
$\sqrt{x_1 - x_2)^2 + (y_1 - y_2)^2} = \sqrt{((-15) - (-20))^2 + ((-20) - (-15))^2}$
The length is $\sqrt{x_1 - x_2)^2 + (y_1 - y_2)^2} = \sqrt{((-15)-(0))^2+((-20)-(-5))^2}$