Find the area A of the polygon with the given vertices

Question

A(-5,-2), B(4,-2), C(4,-7), D(-5,-7)

Answer 1

With these types of questions, you can often figure it out by looking at the numbers... but it's very easy to go wrong. It's much better to do a quick sketch (ideally on graph paper) so you can plot and label the given points, and then draw the lines of the polygon. Then it's easy to see if the shape is a triangle, square or rectangle, which it very often is.

As you are given four vertices, it must be a quadrilateral, but we don't know which kind.

In this case, it's a rectangle.

The area of the rectangle is A = long side x short side

As we're not given any physical measurements (cm, meters, inches, etc.) then the sides are x units and y units, and the area is in square units.

Answer 2

Another way of saying, for example, four minus two, is how far away from two is four? The answer to both is two. Remember that we measure using positive numbers. Even if I walk backward ten feet, I still walk ten feet, not negative ten feet.

We can use the complicated formula, or we can see that A and B are across from each other, as are C and D. How far apart?

|-5 - 4| = 9

We also see that A and D (and B and C) line up vertically. How far apart?

|-2 - (-7)| = 5

9(5) = 45