How to Convert 2D Polygons to Triangles

Triangles are the most fundamental 2D polygon.

It is possible to convert a 2D polygon into a set of triangles that covers the same area. This can be helpful in finding the area of the original polygon, especially if it is an irregular polygon, since it can cut any flat area into triangles whose areas can be calculated by a known formula (base * height / 2). Dividing a polygon into triangles can also help you calculate the total of its internal angles, since the sum of every triangle's internal angles is 180 degrees.

Things You'll Need

• Polygon drawn on paper
• Straightedge
• Pencil

Instructions

1. Draw a line from each concave vertex to another vertex without letting any lines cross or drawing any lines that pass outside of the original polygon. If this process forms any new concave vertices, draw lines from them in the same manner. This will divide a concave polygon into a set of convex polygons. A concave vertex is one that points inward (with an inside angle greater than 180 degrees).

2. Pick one vertex in each non-triangular convex polygon and mark it. If your polygon started out without any concave vertices and you have not yet drawn any lines in it, simply pick one vertex.

3. Draw a line from each marked vertex to every other vertex in its polygon. The result will divide each polygon into a set of triangles.

Tips & Warnings

• If your original polygon is convex, meaning it has no corners that point inward, skip Step 1.

References

• Math Open Reference: Triangles of a Polygon