Question

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),E(10,4.5). The coordinates are measured in miles. What is the area of the city?

Answer 1

41 square miles

Explanation:

There are several ways you can compute the area of this polygon. We have elected to divide it into a rectangle and a triangle.

The rectangle has dimensions 8 × 4.5, so area ...

A = LW = 8 × 4.5 = 36 . . . . . square miles

The triangle has height 2.5 and base 4, so area ...

A = (1/2)bh = (1/2)(4)(2.5) = 5 . . . . . square miles

Then the total area is the sum of these:

36 + 5 = 41 . . . . . square miles