The parallelepiped is a prism which bases and side sides are parallelograms. The parallelepiped can be to straight lines and inclined planes. How to find the area of its surface in that and in other case?
Instruction
1. The parallelepiped can be to straight lines and inclined planes. If his edges are perpendicular to the bases, it is direct. Side sides of such parallelepiped are rectangles. At inclined side sides at an angle to the basis. Its sides represent parallelograms. Respectively, the areas of surfaces of a direct and inclined parallelepiped are defined differently.
2. Enter designations: an and b – the parties of the basis of a parallelepiped; c – edge; h – basis height; S – total area of a surface of a parallelepiped; S1 is the area of the bases; S2 is the area of a side surface.
3. The total area of a parallelepiped represents the sum of the areas of both bases and its side sides: S=S1+S2.
4. Determine the area of the basis. The area of a parallelogram is equal to the work of its basis on height, i.e. ah. Total area of both bases: S1=2ah.
5. Determine the area of a side surface of a parallelepiped of S1. It consists of the sum of the areas of all side sides which are rectangles. The party of AD of a side of AELD is at the same time the party of the basis of a parallelepiped, AD=a. The party of LD – his edge, LD=c. The area of a side of AELD is equal to the work of its parties, i.e. ac. Opposite sides of a parallelepiped are equal, therefore, AELD=BFKC. Their total area – 2ac.
6. The party of the DC side of DLKC is side of the basis of a parallelepiped, DC=b. The second party of a side – an edge. The side of DLKC is equal to AEFB side. Their total area – 2dc.
7. Area of a side surface: S2=2ac+2bc. Total area of a surface of a parallelepiped: S=2ah+2ac+2bc=2(ah+ac+bc).
8. The difference in finding of surface area of a direct and inclined parallelepiped is that side sides of the last are also parallelograms, therefore, it is necessary to have values of their heights. The area of the bases in either case is similarly.