For its occupants to be protected from the elements, it was necessary that the teepee in Exercise 31 be enclosed. Find the amount of area to be covered; that is, determine the lateral area of the rectangular dodecagonal pyramid. Recall that its altitude measures .
The lateral area of the pyramid.
A teepee in shape of a regular pyramid with a dodecagon (12 sides) for the base as below,
and the height of the teepee is and side of the base as and apothem .
A pyramid is made by connecting a base to an apex. The base is flat with straight edges, no curves, hence, a polygon and all other faces are triangles.
A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all congruent.
The lateral area of a regular pyramid with slant height of length and perimeter of the base is given by
The total surface area of a pyramid with lateral area and base area is given by
According to the Pythagorean theorem, in a right-angled triangle
In a regular pyramid, the lengths of the apothem of the base, the altitude , and the slant height satisfy the Pythagorean Theorem; that is,
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