The pyramid is a special case of a cone at which in the basis the polygon lies. Such form of the basis defines existence of flat side sides, each of which in any pyramid can have the different sizes. In this case at calculation of the area of any side side it is necessary to proceed from the parameters (sizes of corners, lengths of edges and an apothem) characterizing its triangular shape. Calculations considerably become simpler if it is about a pyramid of the correct form.
Instruction
1. From statements of the problem the apothem (h) of a side side and length of one of the side edges (b) making it can be known. In a triangle of this side the apothem is height, and a side edge - the party adjoining that top from which height is carried out. Therefore for calculation of the area (s) halve the work of these two parameters: s = h*b/2.
2. If lengths of both side edges are known (b and c), forming the necessary side and also a flat corner between them (γ), the area (s) of this part of a side surface of a pyramid it is possible to calculate too. For this purpose find a half of the work of lengths of edges at each other and on a sine of the known corner: s = ½*b*c*sin(γ).
3. Knowledge of lengths of all three edges (a, b, c), making a side side which area (s) needs to be calculated, will allow to use Heron's formula. In this case it is more convenient to enter additional variable (p), having put all known lengths of edges and having divided result in half of p = (a+b+c)/2. It poluperimetr side side. For calculation of the required area find a root from his work on the difference between it and length of each of side edges: s = √ (p * (p-a) * (p-b) * (p-c)).
4. In a rectangular pyramid to calculate the areas (s) of each of the sides adjacent to a right angle, it is possible on height of a polyhedron (H) and length of the general edge (a) of this side with the basis. Multiply these two parameters and divide result in half: s = H*a/2.
5. In a pyramid of the correct form for calculation of the area (s) of each of side sides it is enough to know perimeter of the basis (P) and an apothem (h) - find a half of their work: s = ½*P*h.
6. At the known number of tops (n) in a basis polygon, the area of a side side (s) of a regular pyramid can be calculated on length of a side edge (b) and size of the corner (α) formed by two adjacent side edges. For this purpose define a half of the work of number of tops of a polygon of the basis at the squared length of a side edge and a sine of the known corner: s = ½*n*b²*sin(α).