Tasks on determination of any parameters of polyhedrons, of course, can cause difficulty. But, if to think a little, it becomes clear that the decision comes down to consideration of properties of separate flat figures of which this solid consists.
Instruction
1. The pyramid is a polyhedron in which basis the polygon lies. Side sides represent triangles with the general top which is at the same time pyramid top. If in the basis of a pyramid the regular polygon, i.e. such at which all corners and all parties are equal lies, then the pyramid is called regular. As it is not specified in a statement of the problem what polyhedron should be considered in this case, it is possible to consider that the regular n-coal pyramid takes place.
2. All edges are equal in a regular pyramid among themselves, all sides are equal isosceles triangles. Height of a pyramid is the perpendicular lowered from top on its basis.
3. Finding of height of a pyramid depends on what is given in a statement of the problem. Apply formulas in which for finding of any parameters of a pyramid its height is used. For example, it is given: V – pyramid volume; S – area of the basis. Use a formula of finding of volume of a pyramid V=SH/3 where H is pyramid height. From here follows: H=3V/S.
4. Moving in the same direction, it should be noted that if the area of the basis is not given, it in certain cases can be found on a formula of finding of the area of a regular polygon. Enter designations: р - poluperimetr the bases (poluperimetr it is easy to find if the number of the parties and size of one party is known); h – a polygon apothem (an apothem is called the perpendicular lowered from the center of a polygon on any of its parties); and - the party of a polygon; n – number of the parties. Thus, p=an/2, and S=ph = (an/2) of h. From where follows: H=3V/(an/2) of h.
5. Certainly, there is a set of other options. For example, it is given: h - pyramid apothem; n - basis apothem; H - pyramid height. Consider the figure formed by the pyramid height, its apothem and an apothem of the basis. It represents a rectangular triangle. Solve a problem with the help of the known Pythagorean theorem to all. In relation to this case it is possible to write down: h²=n²+H², from where H²=h²-n². You need only to take a square root from expression of h²-n².