A church steeple in the shape of a regular square pyramid needs to be reshingled. The part to be covered corresponds to the lateral area of the square pyramid. If each lateral edge measures and each base edge measures , how many square feet of shingles need to be replaced?
The lateral area of the pyramid.
A regular square pyramid as below,
and lateral edge measures and each base edge measures .
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, .
The perimeter of the square is four times the side.
From the given figure
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