Descriptive Geometry/Mathematical Constructions/Polygon Reduction to Triangle

Polygons can be reduced to triangles via polygon triangulation. Using this method, the number of sides a polygon has is gradually reduced to 3. This is convenient for calculating the area of the starting polygon, as triangles' areas are much easier to calculate.


To triangulate a polygon:
1) Create a triangle within the polygon by drawing a line inside the shape to connect the ends of two neinghboring sides.
2) Extend one of the sides touched by the triangle so that it intersects the parallel line.
3) Draw a line connecting the opposite end of the line drawn in step 1 to the intersection drawn in step 2.
4) Repeat steps 1-3 until only 3 sides are left, forming a triangle. It doesn't matter what side is rotated next.
5) The resulting triangle should have the same area as the starting polygon.

http://www.cs.ucsb.edu/~suri/cs235/Triangulation.pdf

http://www-ma2.upc.es/geoc/mat1q1112/triangulacio_de_poligons_EN.pdf

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  Image for Question 1 on Polygon Reduction to Triangle. Answer: http://commons.wikimedia.org/wiki/File:Polygonal_Triangulation_Problem_1_answer.pdf
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  Answer for Question 2 on Polygon Reduction to Triangle. Answer: http://commons.wikimedia.org/wiki/File:Polygonal_Triangulation_Problem_2_answer.pdf