The pyramid represents a polyhedron in which basis the polygon lies, and side sides are the triangles having one general top. The surface area of a pyramid is equal to the sum of the areas of a side surface and basis of a pyramid.
It is required to you
- Paper, handle, calculator
Instruction
1. At first we will calculate the area of a side surface of a pyramid. The side surface is meant as the sum of the areas of all side sides. If you deal with a regular pyramid (that is such in which basis the regular polygon lies, and the top is projected in the center of this polygon), then for calculation of all side surface it is enough to increase basis perimeter (that is the sum of lengths of all parties of the polygon lying in the pyramid basis) by height of a side side (differently the called apothem) and to divide the received value into 2: Sb =1/2P*h where Sb is the area of a side surface, P - perimeter of the basis, h - height of a side side (apothem).
2. If before you any pyramid, then it is necessary to calculate separately the areas of all sides, and then to put them. As side sides of a pyramid are triangles, use a formula of the area of a triangle: S=1/2b*h where b is the triangle basis, and h is height. When the areas of all sides are calculated, it is necessary only to put them to receive the area of a side surface of a pyramid.
3. Then it is necessary to calculate the area of the basis of a pyramid. The choice of a formula for calculation depends on what polygon lies in the basis a pyramid: correct (that is such which all parties have identical length) or wrong. The area of a regular polygon can be calculated, having increased perimeter by the radius of the circle entered in a polygon and having divided the received value into 2: Sn=1/2P*r where Sn is the area of a polygon, P is a perimeter, and r is a radius of the circle entered in a polygon.
4. If in the basis of a pyramid the wrong polygon lies, then for calculation of the area of all figure it is necessary to break a polygon into triangles again, to calculate the area of everyone, and then to put.
5. To finish calculation of surface area of a pyramid, put the areas of a side surface and the basis of a pyramid.