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The distance from the vertex of a regular pyramid to the midpoint of an edge of the base can be found using the Pythagorean theorem. If the height of the pyramid is ( h ) and the distance from the center of the base to the midpoint of an edge is ( d ), then the distance ( D ) from the vertex to the midpoint of the edge is given by ( D = \sqrt{h^2 + d^2} ). This applies to regular pyramids where the base is a regular polygon. The specific values of ( h ) and ( d ) depend on the dimensions of the pyramid and its base.
The surface area of a pyramid is the area of all the faces of the pyramid, for a pyramid with apex in the centre and a regular polygon as its base, (the bottom of a pyramid is the base, it is regular if all sides are the same length) the surface area is: B + 1/2(P * H) where B is the area of the base, P is the perimeter (area around) the base and H is the height of the pyramid.
The volume of a regular pyramid with a square base of 8cm and a slant height of 5 cm is: 64 cm3
An oblique pyramid is either one whose base is not a regular polygon or one whose apex is not vertically above the centre of its base.