Pyramid - a difficult solid. It is formed by a flat polygon (pyramid basis), the point which is not lying in the plane of this polygon (pyramid top) and all pieces which connect pyramid basis points to top. How to find the area of a pyramid?
It is required to you
- ruler, pencil and paper
Instruction
1. The area of a side surface of any pyramid is equal to the sum of the areas of its side sides. Since all side sides of a pyramid triangles, it is necessary to find the sum of the areas of all these triangles. The area of a triangle is calculated by multiplication of length of the basis of a triangle by length of its height.
2. The basis of a pyramid is the polygon. If to divide this polygon into triangles, then it is simple to calculate the area of a polygon as the sum of the areas poluchivshmkhsya at division of triangles on a formula already known to us.
3. Having found the sum of the areas of a side surface of a pyramid and basis of a pyramid, it is possible to find the total area of a surface of a pyramid.
4. For calculations of the area of a regular pyramid use a special formula. Example: Before us a regular pyramid. In the basis there is the correct n-square with the party and. Height of a side side is h (by the way, has the name a pyramid apothem). The area of each side side is equal 1/2ah. All side surface of a pyramid has the area of n/2ha, we calculate by addition of the areas of side sides. na is a perimeter of the basis of a pyramid. We will find the area of this pyramid so: the work of an apothem of a pyramid and half of perimeter of its basis is equal to the area of a side surface of a regular pyramid.
5. As for the area of a full surface, just to side we add the area of the basis, by the principle considered above.