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Wed 21 Sep, 2005 05:23 am
basically, the question im asking is, how do i find the area of a octagonal pyramid that has curved edges, that is to say that the edges curve to a point.
Radius = 20cms
Height = 20cms
this isnt a homework question, its a question my friend who likes maths though of, and me and my other friend couldnt solve it, so now i ask you to help me solve it.
what i have tried is splitting the base up into 8 peices, that give me 8 interconnected issos triangles with base angles of 67.5 and a top angle of 45 degrees, from here i know that the sides of the triangle are 20cms because of the radius, although i need the base...
NOTE : i am trying to find the BASE from this part of it, i have the two side lengths of the triangle, but i need to find the base, i dont know how to do it , so go on and tell me how - i have tried very hard to do this but i cant derive a forumla from what i know.
i have NO CLUE on how to find the arclenght of the curve to the meeting point of the triangles.
so say that i find base length of the base triangle, then what? i then need to find the arc from the base length to the center most point so i can somehow find the goddamn area.
No Need!
You do not need the height from top vertex to the base of a triangle to find its area
Use the Three Side formula instead
If a,b,c are the three sides of a triangle then the
Area of the triangle = Sqrt(s(s-a)(s-b) (s-c))
Where s = semiperimieter of the Triangle = (a+b+c) /2
Hope that helps
edit : hold on that doesnt help at all, i only have the SIDE LENGTHS of the triangle... i am looking for the base, can you plug it into your formula because i dont understand your one, its a bit complicated by the base angles of my triangle are 67.5 and 67.5 and the top angle is 45. therefore i SHOULD be able to find the base, but i cant.
and so i have to somehow find how the arclength of the arc.
if someone could just solve it and write out how they did it for me that would be REALLY helpful.
Ok
Hey I didn't know you don't have all 3 sides
But one of the angle of the triangle is 45 Deg .... That solves your problem completely
Say you have Triangle ABC with Angle at vertex A= 45 Deg
AB = AC = 20
lets draw a perpendiular height segment angle B to side AC.
Say that intersects AC at Z
So we have new triangle ABZ a 45-45-90 triangle
Use Trignometric equations and find height AZ using side AB = 20 (Hypotenuse)
Now you have AZ (Height) and AC (Base).
So Use Base-Height formula and find area.
I'd say there isn't enough information given - in particular how do the edges curve to a point? Do they curve like a circle, an ellisoid and parabola, a hyperbola, is the curve constant or not describle by a polynomic equation.
Without a description of the rate of the curve you problem can only have an upper bound and a lower bound. If you have the curve function - well that's a first or second year Uni maths problem at most unless the curve passes thru a discontinuity - then you have a 3rd year Uni maths problem.
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