Minimum Area

Move the slider and observe the graph. 

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The figure shows a semicircle of radius one and a horizontal line parallel to the diameter. What central angle corresponds to the minimum shaded area? This problem can be solved by either integration or trigonometry. The shaded area is equal to , where  is the central angle. The minimum shaded area occurs when the central angle is .


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Source:

 Abraham Gadalla

"Minimum Area between a Semicircle and a Rectangle"
 http://demonstrations.wolfram.com/MinimumAreaBetweenASemicircleAndARectangle/
 Wolfram Demonstrations Project
 Published: July 1, 2011

Rectangle with Constant Perimeter

Move the dot on Slider A. What do you observe?

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