MIN/MAX area of a rectangle inscribed in a rectangle

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Could someone help me to understand how can I figure it out, how can I create a formula for finding min/max area of a rectangle inscribed in a rectangle, defined by given width and height. Also if it is possible to be inscribed a rectangle at all.

For a private case, when the rectangle is a square, it is pretty easy using the Pythagorean theorem, but for a common case I'm not sure if the inscribed rectangle is really inscribed.
 
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The maximum area is when the inside rectangle and the outside rectangle overlap and and have the same area. The minimum area is when all of the sides of the inside rectangle are length zero.

Is this your question?
 

adjacent

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The maximum area is when the inside rectangle and the outside rectangle overlap and and have the same area. The minimum area is when all of the sides of the inside rectangle are length zero.

Is this your question?
When all the sides are zero length,then it is no longer a rectangle.It's just nothing.Smallest area is when you make the width,infinitely close to zero,(I mean,0.000000001,like this,you can write infinite zeros and then 1.)
 

LCKurtz

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I assume that a rectangle is inscribed in another only all four vertices of the inscribed rectangle touch the outer rectangle. So the outer rectangle itself is the largest and there is either no minimum or a degenerate rectangle having area 0 for the min.
 

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