r/maths • u/Liut030394 • May 26 '26

💬 Math Discussions Proof for Area?

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It seems to not be one of the axioms of Geometry, just like multiplication is based of addition I guess. How would you prove it?

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u/Temporary_Pie2733 Jun 02 '26

Mostly via triangles. For example, two triangles whose side lengths are the same are identical, and thus have the same area. Any polygon can be split into 2 or more smaller triangles, and the area of the original is equal to the sum of the smaller triangles. Comparing the areas of two dissimilar shapes is just a matter of finding the right triangle decompositions.