Pyramid – math help

[Jeff M.]

I need some math help. I'm in the planning stages of making a pyramid. I'd like to make a 9'x9' pyramid with a pole height of 6'. I'm going to sew it ala MLD with the trapezoid shape and attach a small triangle on top. I'm having trouble determining the length of the sides of the small top triangle portion.

The trapezoid part will have a base of 9'(width of the pyramid) with a height of around 5' (the width of the fabric). The dimensions of the entire triangle panel (small triangle + trapezoid) are 9' base, 7.5' height, and 8.75'(8.746…) sides. Can any math whiz out there help me calculate the length of the sides of the small triangle or even just the length of the top of the trapezoid?

[Mark Fowler]

Your trapezoids are actually two right triangles possibly with the top truncated. Halve the base to 4.5ft and then it is just length of hypotenuse = sqrt(x^2 + y^2). Once you have the ratio between the hypotenuse and the appropriate side you can truncate the top of the triangle or just draw a line at the appropriate point perpendicular to the y side.

You need to first calculate the hypotenuse of a triangle with the pole (assuming it is vertical) as the y axis and the distance from the base of the pole to the middle of the fabric side to get the y axis height for the fabric.

[Jeff M.]

I think I've done part of that already. I'm still not quite clear on how to calculate the top triangle part. I've included a quick sketch with dimensions below. It's the sides of the shaded in triangle that I'm trying to calculate. Thanks!

[Lance M]

Jeff,

Here is one of several ways to calculate the sides.

One side is given as 2.5

Second side (small side) is:
4.5 / 7.5 = x / 2.5
x = 1.5

Third side (hypotenuse) is:
sqrt(1.5^2 + 2.5^2) =2.92

equivalent dimensions:

side ,big ,small
side 1 ,4.5 ,1.5
side 2 ,7.5 ,2.5
side 3 ,8.75 ,2.92

Hope this helps. I'm pretty sure I didn't screw up.

[Jeff M.]

Lance,

That does help a lot. I think this was one of the few times I couldn't find the answer through a google search and it was driving me nuts. It's been too long since I've done math.

[Jonathan Edwards]

Here is the shaded area that you requested…BTW if your 90" ( 7'-6") tall and your base is 108" (9'-0") wide your sides will actually be 104 15/16" (8'-8 15/16")

Base = 36"
Sides = 35"

[Paul McLaughlin]

I always like to draw the thing to scale – or full size if you have big enough paper and room to do it. Even if this is just to double-check the calcs, it is worthwhile.

[Jerry Adams]

I agree with Jonathan and Lance

Side of tent has a base of 9' and a height of 7.5'

Little traingle on top has a height of 2.5 feet, so

base of little triangle / 2.5' = 9' / 7.5'

so base of little triangle = 2.5 ' * 9' / 7.5' = 3'

similarlarly, side of little triangle = 8.75' * 2.5' / 7.5' = 2.91' = 34 15/16" (how barbaric that we have to convert to power of two fractions)

[Kevin Beeden]

Google for the geometrical concept of 'similar triangles'.

Since your shaded triangle is the top of the bigger triangle, they are 'similar' (all the angles are the same), and thus all dimensions of the smaller triangle can be simply scaled from the dimensions of the larger triangle, assuming you have one measurement on the smaller triangle to provide a scaling ratio. In this case, you do: 2.5/7.5, or one third.

[Eric Lundquist]

If I understand the design correctly, I think this image will provide you with the right dimensions for your project.

[Jeff M.]

Very cool drawing Eric. That looks correct. Thanks everyone for help on the calculations. I've been going back and forth between wanting a 9×9 and 10×10. I'd like it to fit 3 people comfortably. Any suggestions on what size I should go with? It doesn't look like moving up to a 10×10 adds too much more weight from what I can tell.

[Bill Fornshell]

Hi,

I did something like you are talking about a few years ago. My design approach was a bit different.

This thread shows what I was doing and some comments:

Alphamid and Hex

[Johnny Duke]

Hey Eric what did you use to make this design? Program wise.

[Eric Lundquist]

@Johnny,

I used Google SketchUp for the layout. It definitely helps with not having to do a lot of math to figure stuff like this out.

[Elliott Wolin]

I'm sure you know this, but to be on the safe side:

Don't forget the seam allowances, 3/4" at each edge to make 1/2" flat-felled seams. Also remember that the upper triangle lower edge has to be a little wider than the top edge of the lower trapezoid. That is, you have to make the upper triangle and the lower trapezoid taller and extend the angles of the sides to match.

Also, when the seam is sewn the overlap can look a little funny. You'll have to trim it to get a straight edge. If you are doing a catenary cut then you'll be trimming it plenty.

[Jerry Adams]

If you're a true wizard you'll get the seam allowance right and the edges will line up after you sew the two pieces together

[Elliott Wolin]

Alas, a wizard I am not…

One more thing, don't forget about 1.5" extra at the bottom for a doubled 3/4" hem.

[Jerry Adams]

I just use 1/2" seam allowance

Fold over twice for 1/4" hem or flat felled seam

[Elliott Wolin]

On my 11' pyramid I used a doubled 3/4" hem to give a good base for all the tie-outs and things.

I also used 1/2" flat-felled seams for lots of strength in wind or under snow loads. This means a 3/4" seam allowance on both parts.

I suppose I overdo it, but the difference in weight is negligible, and it's easier to sew the larger seams for us clumsy folks with failing eyesight…

[Author]

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