In a topographical map of a city, the vertices of the city limits are a (10, 9), b (18, 9), c (18, 2), d (14, 4.5), and e (10, 4.5). the coordinates are measured in miles. what is the area of the city?

The first thing to do is to plot the points to see the figure to which you want to find the area.
 Looking at the figure we see that we can divide the figure in two:
 Triangle and rectangle.
 Area of the triangle: (1/2) * (4) * (2.5) = 5 mi^2
 Area of the rectangle: (8) * (4.5) = 36 mi^2
 Therefore the total area is
 At = 36 + 5 = 41 mi^2
 Graphic attached.