The parallelepiped is a special case of a prism. Its distinctive feature consists in a squared shape of all sides and also in parallelism of each couple standing the friend opposite to the friend of the planes. There is the general formula for calculation of the volume concluded in this figure and also several its simplified options for special cases of such hexagon.

## Instruction

1. Begin with calculation of the area of the basis (S) of a parallelepiped. The opposite sides of the quadrangle forming this plane of a volume figure by definition have to be parallel, and the corner between them can be any. Therefore determine the area of a side by multiplication of lengths of her two adjacent edges (an and b) on a sine of the angle (?) between them: S=a*b*sin (?).

2. Increase the received value by parallelepiped edge length (c), a forming the general three-dimensional corner with the parties and b. As the side side which possesses this edge by definition has to be not necessarily perpendicular to the parallelepiped basis, increase the calculated value also by a sine of the angle of an inclination (?) of a side side: V=S*c*sin (?). In a general view the formula of calculation of volume of any parallelepiped can be written down so: V=a*b*c*sin(?)*sin (?). For example, let in the basis of a parallelepiped the side which edges have lengths of 15 and 25 centimeters and a corner between them in 30 ° lies, and side sides are inclined on 40 ° and have an edge, of 20 cm. Then the volume of this figure will be equal 15*25*20*sin (30 °) to *sin (40 °)? 7500*0.5*0.643? 2411.25 cm?.

3. If it is necessary to calculate the volume of a rectangular parallelepiped, then the formula can be simplified considerably. Owing to the fact that the sine 90 ° is equal to unit amendments on corners can be removed from a formula, so, will be to multiply enough lengths of three adjacent edges of a parallelepiped: V=a*b*c. For example, for a figure with lengths of edges used in an example on the previous step, volume will be 15*25*20 = 7500 cm?.

4. The formula for calculation of volume of a cube - a rectangular parallelepiped which all edges have identical length is simpler. Build length of this edge (a) a cube to receive required value: V=a?. For example, at a rectangular parallelepiped which lengths of all edges are equal to 15 cm the volume will be equal 153=3375sm?.