Calculation of surface area of the main stereometric figures is made by means of a uniform technique. There is an area of the basis or the bases of a figure, then the area of each of side sides. After that the areas develop. For a prism and a regular pyramid there are separate formulas, as well as for rotation bodies (cylinder and a cone). The area of the sphere is calculated by different way.
It is required to you
- Ruler, formulas of finding of the areas of polygons
Instruction
1. To calculate prism surface area, find the area of one of its bases. Use a formula depending on what is a geometrical figure (polygon). Then, find all parties of the basis and, having put them, receive its perimeter. Having increased perimeter by length of one from side edges (they are equal), calculate the area of a side surface. The surface area of a prism will be equal to the sum of the area of a side surface and the doubled area of the basis (as their two) to S=Sb +2 • So.
2. Calculation of surface area of any pyramid is made by addition of the area of the basis, and each side. For a regular pyramid (when the regular polygon is its cornerstone, and the top is projected on crossing of its diagonals), it is possible to use special formulas.
3. Find the area and perimeter of the basis of a regular pyramid. Calculate the area of a side surface, having increased a half of perimeter by an apothem of a side side (its height) of S = 0.5•P • a. Find an apothem as height of an isosceles triangle which the side side of a regular pyramid is. Put the area of the basis and side surface and receive the area of a full surface.
4. To find the area of a full surface of a circular cylinder, find the sum of its radius and height which represents a piece the turned-out result connecting the centers of circles which are the cylinder bases and increase by the radius and number 6.28, S=6.28 • r • (r+h).
5. Find the surface area of a circular cone through the radius of its basis and forming. For this purpose the sum of radius and forming (the piece connecting cone top to any point of a circle of the basis), increase by the radius and number 3.14. S=3.14 • r • (r+l).
6. For finding of surface area of the sphere find its radius. Then the area will be equal to the work of a square of radius on number 12.56 S=12.56 • r².