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Mean Triangle Area

The mean triangle area A^_ is the average area of a triangle in triangle picking within some given shape. As summarized in the following table, it is possible to compute the mean triangle area in closed form for triangle picking for some simple shapes.

shapeA^_
ball triangle picking(9pi)/(77)
circle triangle picking3/(2pi)
decagon triangle picking1/(18000)(745+262sqrt(5))
disk triangle picking(35)/(48pi)
equilateral triangle triangle picking1/(12)
hexagon triangle picking(289)/(3888)
octagon triangle picking1/(2304)(97+52sqrt(2))
pentagon triangle picking1/(180)(9+2sqrt(5))
square triangle picking(11)/(144)
tetrahedron triangle picking0.1811+/-0.0012

See also

Mean Line Segment Length, Mean Tetrahedron Volume, Polygon Triangle Picking, Triangle Picking, Triangle Triangle Picking

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Cite this as:

Weisstein, Eric W. "Mean Triangle Area." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MeanTriangleArea.html

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