Direct prism — a polyhedron with two parallel bases polygons and side sides lying in the planes perpendicular to the bases.
Instruction
1. The bases of a direct prism are polygons equal each other. Side edges of a prism connect tops of the top and lower polygon and are perpendicular to the planes of the bases. Therefore, side sides of a direct prism are rectangles. These rectangles are formed everyone by two side edges of a prism and two parties of a figure of the basis (top and lower).
2. Prism section the plane parallel to the bases, forms the figure equal to the basis. All parties of such section are known or are defined in the course of the solution of a polygon.
3. Prism section the plane perpendicular to the bases, forms a rectangle within a polyhedron. Two parties of a rectangle are equal in this section to side edges of a prism. Two other parties of section lie in the planes of the bases and are diagonals of polygons if connect tops of a figure of the bases. Or the considered parties of section can connect any points on the parties of a polygon. Then for their location it is necessary to draw auxiliary lines in a basis polygon so that the required party of section became the party of a triangle, in two other parties are the parties of the basis of a prism. Finding of the unknown party of section comes down to the solution of a triangle.
4. Prism section the plane located under any corner to the bases and crossing the planes of the bases outside a polyhedron is a polygon with the number of the parties equal to number of the parties of the basis. Each party of the figure formed in section needs to be found separately. The required parties of this any section divide each side side of a direct prism into two rectangular trapezes. Pieces of side edges of a prism are the parallel bases of trapezes, the party of the basis in a trapeze is the party and at the same time height. The required party of section in each trapeze is the fourth party. Thus, the problem of finding of the parties of section of a direct prism any inclined plane comes down to calculation of the party of a rectangular trapeze.