Math CentralQuandaries & Queries


Question from Karen, a parent:

I am going to make my kids a six sided tipi (pyramid) I have a 5 foot tall central pole, and I would like the floor area to be 6 feet across. How do I work out what size to cut each fabric panel to make this happen?

Hi Karen,

I drew a sketch of your tipi.

tipi 1

RS is one side of the base, M is the midpoint of RS, B is the base of the central pole and T is its tip. The length of TB is 5 feet and the length of BM is 3 feet. Triangle TBM is a right triangle so Pythagoras theorem gives is

|TM|2 = |TB2| + |BM|2 = 52 + 32 = 34

and hence

|TM| = 5.83 feet or 5 feet 10 inches.

Now turn your attention to the hexagonal base.

tipi 2

The measure of angle SBR is 360o/6 = 60o. Thus the measure of angle SBM is 30o and the measure of angle MSB is 60o. You know the length of BM is 3 feet and a little knowledge of trigonometry tells you that the length of MS is √3 feet. Hence the triangular fabric piece TRS has base length 2 √3 = 3.46 feet or 5 feet 6 inches and height MT 5 feet 10 inches.

If you want to know the length of the side TS you can use Pythagoras theorem again with triangle TMS to get

|TS|2 = |MS|2 + |TM2| = (√3)2 + 32 = 41

and hence

|TS| = 6.40 feet or 6 feet 5 inches.

Good luck i this project,

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