The four points (−2, 5), (−2, −1), (6, −1), and (3, 5) are the vertices of a polygon. what is the area, in square units, of this polygon?

Look at the picture.

The polygon is a right-angled trapezoid.

The area is:


The points (-2,-1) and (6,-1) lie on the same horizontal line, so the distance between them is 6-(-2)=6+2=8. The length of a is 8 units.
The points (-2,5) and (3,5) lie on the same horizontal line, so the distance between them is 3-(-2)=3+2=5. The length of b is 5 units.
The points (-2,5) and (-2,-1) lie on the same vertical line, so the distance between them is 5-(-1)=5+1=6. The length of h is 6 units.



The area is 39 square units.