Prism call a polyhedron in which basis equal polygons lie. Side sides of this solid represent parallelepipeds. They can be perpendicular to the bases, and in this case call a prism a straight line. If sides have some corner with the basis, the prism is called an inclined plane. The area of a side surface is defined in these cases differently.
It is required to you
- - sheet of paper;
- - handle;
- - calculator;
- - a prism with the set parameters;
- - theorems of sine and cosines in case of an inclined prism.
Instruction
1. Construct a prism with the set parameters. The type of this solid, the sizes of the parties of the basis, height and a tilt angle of side edges have to be known to you at least. The last condition is necessary for an inclined prism.
2. Calculate the area of a side surface of a direct prism. According to definition, at this solid the side edges are perpendicular to the basis. It means that perpendicular section is congruent to both polygons lying in the basis. That is the area of a side surface of a direct prism is calculated by multiplication of perimeter of the basis by height. It can be expressed a formula S=P*h where P — perimeter of any of the bases. Find it, having put lengths of all parties. In certain cases it is enough to find poluperimetr and to increase it by 2.
3. To find the full surface area of a direct prism, add on the doubled area of the bases to the received size. If in the basis the triangle or a quadrangle which parties are known to you lies, the area is calculated on a usual formula for this geometrical figure. But the polygon can be and more difficult. In this case make additional constructions, having dismembered it on figures with parameters known to you or those which can be found rather easily.
4. For calculation of the area of a side surface of an inclined prism it is necessary to construct perpendicular section. This such section which is perpendicular to all edges. It it is possible to arrange so that it cut from some sides the triangle formed by an edge between the basis and a side side, a part of a side edge and the line of perpendicular section. If the basis is the wrong polygon, the lines of side section belonging to different sides it is necessary to calculate separately. It can be done according to theorems of sine and cosines, using the set tilt angles.
5. Having calculated the parties of perpendicular section, put their lengths and receive perimeter. Having increased it by assigned altitude, you receive the area of a side surface of an inclined prism. 'S=P*h. P' in this case means perimeter of perpendicular section.