Cutting a Triangle from a Square

Appropriate Level:  Calculus (1 or 2, depending on how your courses are divided).

The Question: You start with a unit square (say a piece of paper).  Choose two adjacent sides of the square and randomly pick a point on each.  Connect the two points with a line and cut along that line, thus removing a triangle (it could be a degenerate triangle) from the piece of paper.  Let A be the area of the triangle that has been removed.

What is the smallest A can be?

What is the largest A can be?

What is the probability that A is less than 1/4?  In particular, is this probability equal to 50%? (after all, 1/4 is half way between 0 and 1/2).

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About Aaron

I like good math problems.
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