The side of a cube represents a square which diagonal divides it into two equal rectangular triangles, being their hypotenuse. For this reason all formulas used here to a degree are based on application of Pythagorean theorem. Depending on the available data you will be able to find the area of a side (square) of a cube in several various ways.
It is required to you
- The calculator or the computer with the appropriate program
Instruction
1. If cube surface area is set, then this value is enough to be divided into 6 as the official name of this geometrical figure - a hexahedron (a hexagon with equal sides). Find the area of the party of a cube on a formula: Sgr = Sp/6, gdesgr – the area granisp – the area of all surface of a cube
2. If the cube edge length, then the area of a side is known to you you will find, having squared this value. The parties of a cube are equal, and adjacent edges of a cube in one plane are the parties of a square. Use a formula: Sgr = a2, gdea – cube edge length
3. At the set perimeter of the square representing a cube side it is possible to calculate the area, having divided perimeter into four and having squared the received result. It is a special case of finding of the area on edge length. Use a formula: Sgr = (P/4)2, gder – perimeter of the square which is a cube side
4. If cube side diagonal length, then, proceeding from Pythagorean theorem is known to you, this value should be squared and divided into two. You will find the area on a formula: Sgr = (d2)/2, gded – cube side diagonal length
5. Knowing length of big diagonal of a cube (it is the piece which is connecting tops, symmetric concerning the center of a cube, not lying in the plane of any of its parties), you will be able to find the area of a side, having divided diagonal length into a square root from three (cube edge length will turn out) and having squared result: Sgr = (D / √ 3)2, gded – length of big diagonal of a cube
6. On the known volume of a cube it is also possible to find the area of a side. For this purpose take a cube root from the volume of a cube and square result: Sgr = (3√V) 2, gdev – cube volume