Find the area of a polygon with vertices at (1,3), (7,3), (7,7), and (4,7).

(1,3) and (7,3) falls on the same horizontal line. hence, the distance is just equal to 6 units. (7,3) and (7,7) meanwhile lie on the same vertical line. hence the distance is 4. (7,7) and (4,7) lie on the same horizontal line with a distance of 3. 

Finally, to get back to point (1,3) - (4,7) > (1,3), 3 to the left and 4 down, the diagonal being 5. 
6+4+3+5= 10 + 8 = 18.

I graphed the points and connected them. I found two shapes. A rectangle and a right triangle.

I individually computed its area.

Rectangle = length * width = 4 * 3 = 12 square units

Triangle = ab/2 = (4 * 3) / 2 = 12/2 = 6 square units

12 + 6 = 18 square units