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Topic: Venn Diagram: Area of Equilateral Circular Triangle
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 VennJon Posts: 3 Registered: 3/23/07
Venn Diagram: Area of Equilateral Circular Triangle
Posted: Mar 23, 2007 10:52 AM

In need help calculating the area of the seven sections of a Venn Diagram.

I have three overlapping circles (A,B,and C) arranged in a Venn Diagram. Each circle overlaps exactly the same amount with equal radii, and all sides of the remaining circular triangles are of equal length (Equilateral Circular Triangle).

There are three smaller, intersecting sections (AB,BC, CA,) and the middle section (ABC) is slightly larger that the middle sections.

Each circle has the follow approximate measurements:
Circumference: 31.42
Diameter: 10
Area: 78.5

I found a document that contains the formula for such a problem, but I do not fully understand it. He says to treat the intersecting sections as triangles and the corners as circular elements. But when he gets into the actual formula, I am lost because he strikes off on tangents.

Here is the doc:
http://203.10.217.104/publications/4815/DSTO-TN-0722.pdf

Page 19 of 30 of the document contains the circle problem I am after, but I can't figure out which formula to use.

Can someone help me sort it out? I am looking for the formula for each of the seven sections so I can determine the area of each section (A,B,C,AB,BC,CA,ABC).

Thanks!!!