OK, could likely figure it out, but why do the work when somebody here already has the answer, or, treat this a a quiz.
Duodecahedron dome (scored a steel corner tie plate kit set at a garage sale fo $5). County allows 200 sq ft building without a permit. By one interpretation, this is floor area which allows a good sized dome, another interpretation is ‘under roof” which would be a smaller dome. The floor case is trivial as the floor is a pentagon, easily figured. Could alway really push the ‘point’ and set the dome on a small area of a corner, but likely get building compliance dept. real unhappy.
For the “area under roof” size, what is the length of the side of the pentagons to give 200 sq ft “under roof” ?
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A pentagon would consist of five equilateral triangles.
200 sf means forty sf for each triangle. Th eformula for A of a triangle is 1/2H x B
B is same as a side of the triangle or side of the pentagon, but darned if I can remember how to find the height to plu into the forrmula...
OK - it's that old AA + BB + CC
http://kjmaclean.com/Geometry/PentArea.html
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here we go - google can solve anything, I guess
http://www.infoplease.com/ipa/A0001726.html
Area = 1.720 times the side of the triangle squared
Given Area of 200 sf
200/1.72 = ss
116.2791 = ss
10.7838 = side of the pentagon
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Piffin I may have missed something.
The the vertex angle for the pentagon sector triangles is 360 divided by 5 or 71 degrees. That leaves 54 degrees for each base angle. They are not equilateral but rather isosceles
HarryD
Right, they are not equilateral - only on e two sides, not three.BTW, 360/ 5 = 72° rather than 71another site showed the geometry as ten right triangles formed by bisecting the isoceles with the height line, and calculating from there
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Got me curious as to the tie plate kit set.
Someone has been manufacturing the 'starplate' connectors as a homeowner kit for a small shed dome for quite a while now, something like decades.
Seems to have caught on and are fairly popular.
Might this be what you have?
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Some guys get really creative with their dome construction techniques...
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Why not go with "mercaterian" concept? Orange rind and hoops?
Spheramid Enterprises Architectural Woodworks
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You mean orange grinds and hops?
sobriety is the root cause of dementia.
yeah, dats da ticket
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I don't understand the difference between the floor area and the area under roof.
Slightly different story ... "investigative report" on local tv this week ... house starts getting built on a vacant lot, neighbor thinks it's too close to the property line. House wass fully permitted and inspoected. At some point, after the roof is on, the inspector notices that it's 2 feet off the PL rather than 5 ft. Neighbor files a complaint. Building officials etc convene an investigation, and decide to grant a variance. It's a single story 1500+ sf basic house. Local politics prevails again.
I'm sorry, I thought you wanted it done the right way.
Some dome styles if built without having a riser wall underneath them could be all roof to the ground when another style could have some sides of the dome inverting back towards it's center before it meets the ground.
As if you were to take a soccer ball and cut it horizontally 5/8ths of the way down from the top, the base that then would meet the ground as the floor area will have less area than the horizontal point at 1/2 or 3/8ths.
I wonder if the the code folk might try to call that a cantilever or would they have to rewrite their wording for dome structures?
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Edited 5/8/2005 10:57 am ET by the razzman
We call that "over center". My house is that way. It certainly comes into play with setbacks, be/c the measurements are from the part of the building closest to the boundary. I'd think whatever rules apply to bay/bow windows--or any projection from the building--could also apply here.
If it were a circle, it would be just under 16' dia.