Q:

How many edges does a pentagonal pyramid have?

A:

A pentagonal pyramid is characterized by six faces, six vertices and 10 edges. This three-dimensional polyhedron is a type of pyramid containing five triangular lateral faces and one pentagonal face, which is the base of the pyramid.

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Pyramids are solid geometric figures made up of planar surfaces called "faces" that are bounded by line segments referred to as "edges" or "sides." The points where the edges of the faces meet are called "vertices" or "corner points." The faces are all triangular polygons, which are two-dimensional shapes that are completely enclosed. The intersection point of the lateral faces is called the apex of the pyramid, located above the base. Pyramids are named based on the shape of their bases.

The Swiss mathematician Leonhard Euler devised a formula for computing the number of faces, vertices and edges for most three-dimensional polyhedrons. Known as Euler's formula, this mathematical equation is given as F + V - E = 2, where "F" indicates faces, "V" denotes vertices and "E" represents edges. The sum of the faces and vertices minus the number of edges is always equal to 2. The formula for calculating the number of edges can then be expressed by the derived equation F + V - 2 = E. By substituting the correct values for a pentagonal pyramid such that 6 + 6 - 2 = E, the number of edges is equal to 10.

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