Math and Logic

How Much Area Is Left?

The tick marks in the diagram below represent 12,13,14,,111\frac12, \frac13, \frac14,\ldots , \frac{1}{11} of the side length of the square. As you change the value of the slider, how does the diagram change? How does the base of the triangle at the bottom of the square change? How does the height of the triangle change? Are the base and height somehow related?

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