How to calculate the height of the pyramid

Problem to the determination of any parameters of the polyhedrons, of course, can cause obstruction. But, if you think a little, it becomes clear that the decision boils down to a consideration of the properties of certain plane figures that make up this geometric solid.

Instruction

1. Pyramid – a polyhedron whose base is the polygon. The side faces represent triangles with a common vertex that is both the pinnacle of the pyramid. If the base of the pyramid lies a regular polygon, i.e., one in which all angles and all sides are equal, then the pyramid is called regular. Since the problem statement does not specify what kind of polyhedron should be considered in this case, we can assume that there is a right polygonal pyramid.
2. In a right pyramid all edges are equal, all faces are equal isosceles triangles. Height of a pyramid is the perpendicular from the vertex to its base.
3. Finding the height of a pyramid depends on what is given in the problem statement. Use of the formula in which to locate any parameters of the pyramid is the height. For example, given: V is the volume of the pyramid's square base. Use the formula for finding the volume of a pyramid V=SH/3, where H is the height of the pyramid. Hence: H=3V/S.
4. Moving in the same direction, it should be noted that if the footprint is not given, it in some cases, you can find the formula for finding the area of a regular polygon. Type designation:R - properiter base (properiter easy to find if you know the number of sides and the size of one side);h – apofema polygon (apofema is called the perpendicular from the center of the polygon to any of its sides); a side of the polygon;n = number of sides.Thus, p=an/2, and S=ph= (an/2)h. Whence it follows that: H=3V/ (an/2) h.
5. Of course, there are many other options. For example, given:h - apofema of the pyramid;n is apofema base;H - the height of the pyramid.Consider the shape formed by the height of the pyramid, its apofema and apofema base. It is a right triangle. Solve the problem using the well-known Pythagorean theorem. In this case we can write h2=n2+H2, where H2=h2-n2. You just have to take the square root of the expression of h2-n2.