Question 1149554
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The solution currently posted from tutor @Alan is incorrect.<br>
To use that method, as he states at the end of his post, the coordinates of the vertices of the polygon (rectangle) have to be in order.  The way he ordered the coordinates, they are not.<br>
Wait and see if he corrects his response; his method is a good one to know for finding the area of any polygon.<br>
For this example, knowing that the polygon is a rectangle (area length times width), we can use the distance formula to find the lengths of two adjacent sides and multiply those two lengths to get the area.<br>
One side: (-4,0) to (4,4); length {{{sqrt(8^2+4^2) = sqrt(80) = 4*sqrt(5)}}}
Adjacent side: (-4,0) to (-6,4); length {{{sqrt(4^2+2^2) = sqrt(20) = 2*sqrt(5)}}}<br>
Area: length * width = {{{(4*sqrt(5))*(2*sqrt(5)) = 8*5 = 40}}}<br>
ANSWER: 40 square units<br>