Universal area forumula for equilateral + equiangular shapes?

This is a discussion on Universal area forumula for equilateral + equiangular shapes? within the A Brief History of Cprogramming.com forums, part of the Community Boards category; I am making a program based on geometry (learning purposes) and now am wondering if there is such formula/equation to ...

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    Universal area forumula for equilateral + equiangular shapes?

    I am making a program based on geometry (learning purposes) and now am wondering if there is such formula/equation to find the total area of shapes with equal sides and angles. I don't want to program the calculator where I must define seperate equations for each shapes such as triangles, squares, pentagons, as it'll be practically useless, time consuming, and restrictive.

    My problem is that I don't ever recall learning such equation in Geometry, equations from google didn't work, and the equation my current Math teacher formulated in 2 minutes didn't work either. Specifically, these equations didn't not work with triangles.

    So, my question is not what is the equation to find the area of equilateral shapes, but whether there is. I want to find out the equation myself if it does exist, assuming it does not require significant math knowledge beyond that of an average person.

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    and the hat of wrongness Salem's Avatar
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    Thanks, I now actually know it exists ^_^

    I'm thinking it has to do with determining how many triangles are able to fit inside the shape...

    My math teacher also told me the same concept, except his equation was a bit hasty I suppose.

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    S Sang-drax's Avatar
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    The area of the parallellogram given by two vectors from the origin is the determinant. The triangle area is half that.

    The attached picture shows how to partition a polygon to be able to use determinants to calculate the area.
    Attached Images Attached Images  
    Last edited by Sang-drax : Tomorrow at 02:21 AM. Reason: Time travelling

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