Find area of rectangle with vertices (5,2) (5,-6) (0,-6) (0,2)

Question

I know you can solve this with the distance formula but are there any faster ways?

Answer 1

It depends on what you mean by "this distance formula."  Do you mean √((x₂-x₁)²+(y₂-y₁)²)?

 

I would say just do a quick plot of the points, to see how they form the vertices of a rectangle.  (5,2) and (5,-6) have the same x and different y, so (given that the rectangle has sides parallel to the x and y axes) this represents a "vertical" side of the rectangle, and the length is the distance from 2 to -6, which is 2-(-6) = 8.  The (5,-6) and (0,-6) have the same y but different x, so this is a "horizontal" side of the rectangle.  Its length is the distance from 5 to 0, which is 5.  So the rectangle has side lengths 8 and 5, and you can calculate the area.

 

If you use a quick sketch to guide you, this may be "easier" than using the distance formula, even though it takes longer to say in words.

Answer 2

That's the best way.  There is another way but it's not intuitive.