We start with a rectangle which has area 



Then we round off the corners, which means that we
subtract the 4 little corners that we round off from
the original area which is .



Next we draw in the quadrants of a circle of radius r to help us
see how much was subtracted from the corners in the rounding 
process.



Now we look at just those quadrants of a circle:



Now we put the four together and have a circle inscribed in a square



Now we can see how much we have to subtract off from the
area of the original rectangle whose area is 

We have the area of a square whose side is twice the radius r.
That's .  From that we subtract the area of the
circle , and get .

That means the area of the rounded metal plate is xy minus
the area of those corners.







We can factor out the r2 in the last two terms:

  <--expression for A

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To get your answer for r, go back to the previous step:











Edwin