I have the length of two corners of a rectangle, how do I find the area?
Corner of bottom left= (y1,x1)
Corner of top right= (y2, x2)

SIMPLE !
 area of a rectangle is Length * Breadth

so.....
 [(y1+x1)* (y2+x2) ]

>I have the length of two corners of a rectangle

Don't you mean the co-ordinates of two corners of a rectangle ?
( same as 'length' from (0, 0) Origin )

If so : Width = x2 - x1     ( it could be negative )
        Height = y2 - y1    ( ditto )
        Area = (x2 - x1) * (y2 - y1)
        If Area < 0 Then Area = - Area

Frde is correct.

i think it would be simple for you to imagine it on a graph sheet
>mark those 2 corners
now draw perpendiculars from x,y axes to those 2 points
now you have the complete rectangle
thus the area can be found
as now we know all its  co ordinates

Simple Answer
Let A(y1,x1) and C(y2,x2) be two diagonally opposite corners of a rectangle

               
        A(y1,x1) -------------------- D(y2,x1)
                 |                   |     
                 |                   |
                 |                   |
                 |                   |
        B(y1,x2) -------------------- C(y2,x2)

So we can easily get the other 2 cordinates i.e B(y1,x2) and D(y2,x1)

now lenght of AB =sq.Rt.(sq.(y1-y1)+sq.(x2-x1))
and breath of BC =sq.Rt.(sq.(y2-y1)+sq.(x2-x2)

Now the area of rectangle is = lenght * breadth
                             =length Ab * breath BC
         answer is           = (sq.Rt.(sq.(y1-y1)+sq.(x2-x1))*        
       dsq.Rt.(sq.(y2-y1)+sq.(x2-x2) )

So final answer is (sq.Rt.(sq.(y1-y1)+sq.(x2-x1))*
sq.Rt.(sq.(y2-y1)+sq.(x2-x2) )

Notations used : Sq.Rt.() means Square Root                 
                 Sq.() means square