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#1
08-27-2019, 03:16 AM
 lahanroyal Windows 7 64bit Office 2007 Novice Join Date: Jul 2019 Posts: 4
Formula Creation

I want to input the four or more sides of a polygon and want the area to be calculated accordingly.
Say for example, sides a,b,c,d & e to be input and the area of that polygon to be calculated automatically.
#2
08-27-2019, 05:41 AM
 ArviLaanemets Windows 8 Office 2016 Expert Join Date: May 2017 Posts: 467

As you say you want to calculate a polygon (i.e. all sides can be of different length, and corners may be not 90º), you can't! Not enough info with lengths of sides only.

An example: When all sides are equal, the area of 4-side polygon can be anything between 0 and SideLength*SideLength.
#3
08-27-2019, 05:48 AM
 lahanroyal Windows 7 64bit Office 2007 Novice Join Date: Jul 2019 Posts: 4

I currently use an app that allows me to enter four sides irrespective of the shape of the polygon and it provides me with an area. But, yes, the app has an interface which asks me to select the type of polygon that im wishing to find the area of. there are about 50 odd shapes of which the app provides areas. I could share the name of the app with you just for reference. The app is: Area Calculator by NSDev (Nihon System Developer Corp.)
#4
08-27-2019, 11:10 PM
 ArviLaanemets Windows 8 Office 2016 Expert Join Date: May 2017 Posts: 467

Any polygon can be looked at as a collection of triangles with common top opposite of base, and with one side of polygon as base. Area of polygon equals to sum of areas of those triangles. Area of triangle equals to (1/2)*LengthOfBase*HeightOfTriangle. So generally your task will be to determine where is the common top for all triangles, and how to calculate the height of every triangle. The calculation of height depends on:
1. the number of sides/corners;
2. length(s) of sides;
3. symmetry of polygon.
3a) When polygon is fully symmetric (it is symmetric for every diagonal, i.e. axis drawn through certain central point - e.g. a square), 2 first conditions are enough;
3b) When polygon is symmetric for 2 different diagonals intersecting at 90º, and all sides are equal (e.g. romb), you need additional parameter (how many degrees is at one corner, how many sides are there, and what is the length of side;
3c) The number of needed parameters will grow with number of different diagonals and number of different side lengths growing;
3d) The most complex will be case when you have no symmetry at all. I'm not sure about this, but probably you need the number of sides, lengths of all sides, and degrees for (NumberOfSides - 1) corners.

 Tags area, formula, polygon

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