The area of a pyramid usually is understood as the area of its side or full surface. In the basis of this solid the polygon lies. Side sides have triangular shape. They have the general top which at the same time is also pyramid top.
It is required to you
- - sheet of paper;
- - handle;
- - calculator;
- - a pyramid with the set parameters.
Instruction
1. Consider the pyramid given in a task. Define, the regular or wrong polygon lies in its basis. At correct all parties are equal. The area in this case is equal to a half of the work of perimeter on the radius of an inscribed circle. Find perimeter, having increased length of the party of l by the number of the parties of n, that is P=l*n. It is possible to express the area of the basis a formula So =1/2P*r where P - perimeter, and r - the radius of an inscribed circle.
2. The perimeter and the area of the wrong polygon are calculated differently. The parties have different length. To count perimeter, it is necessary to put all pieces limiting the basis. For calculation of the area execute additional construction. Divide the wrong polygon into figures which parameters are known to you, and you can easily find the area, using the most widespread formulas and trigonometrical functions.
3. The side surface of a pyramid represents the sum of all side sides. At a regular pyramid height falls in the center of the regular polygon lying in the basis. For descriptive reasons it is very useful to construct heights of the pyramid and one of its sides. Connect a point of intersection of the second height with the lower side to the center of the basis. At you the rectangular triangle in which you need to calculate the hypotenuse which is at the same time and height of a side side anyway will turn out. Make it, using parameters known to you (for example, height of the pyramid and radius entered in a circle basis polygon).
4. Knowing height of a side side of a regular pyramid, calculate the area of a side surface. It is equal to a half of the work of perimeter of the basis on height of a side side, that is it is possible to calculate it on a formula Sb =1/2P*h where P - perimeter already known to you, and h - height of a side side.
5. Calculation of a side surface of the wrong pyramid will involve from you several big costs of time. It is equal to the sum of the areas of all side sides. Remember what the area of a triangle is equal to. It can be found on a formula S=1/2l*h, that is the semi-work of the basis of a triangle on its height.
6. Find the area of a full surface of a pyramid. For this purpose put the areas of the basis and a side surface already known to you.