Given a polygon with known perpendicular lines from any point inside the polygon, make a statement about the height

 May 13, 2018
edited by Rollingblade  May 13, 2018

Hi Rollingblade!


Melody made a similar answer here: https://web2.0calc.com/questions/weekly-cycle-challenge-2-help 

I was thinking about Melody's answer and was thinking about how to generalize it. Here is what I have:


Using the hexagon problem: 


The area of the hexagon is equal to the sum of the six triangles constructed from connecting the point inside the hexagon to the 6 vertices. 




The area can also be expressed as the sum of the areas of the 6 equilateral triangles. 




Since these two expressions are equal, we get:




This is true for any polygon. 


n-sided polygon:




Where h is the height, and a - z are the known perpendicular lines from any point.

 May 13, 2018
edited by GYanggg  May 13, 2018

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