The pyramid is meant as one of types of polyhedrons in which basis the polygon lies, and its sides are triangles which connect in uniform, general top. If from top to lower a perpendicular to the pyramid basis, the turned-out piece will be called pyramid height. To determine pyramid height very easily.
Instruction
1. The formula of finding of height of a pyramid can be expressed from a formula of calculation of its volume: V = (S*h)/3 where S is the area of the polyhedron lying in the basis of a pyramid, h - height of this pyramid. In that case, h can be calculated so: h = (3*V)/S.
2. In case in the basis of a pyramid the square lies, length of its diagonal and also length of an edge of this pyramid is known, then height of this pyramid can be expressed from Pythagorean theorem, a triangle which is formed by a pyramid edge, height and a half of diagonal of a square in the basis is a rectangular triangle. Pythagorean theorem says that the hypotenuse square in size is equal in a rectangular triangle to the sum of squares of its legs (a² = b² + with²). A pyramid side - a hypotenuse, one of legs - a half of diagonal of a square. Then length of an unknown leg (height) is on formulas: b² = a² - with²; with² = a² - b².
3. That both situations were clearest and clear, it is possible to review couple of examples. Example 1: The area of the basis of a pyramid of 46 cm², its volume it is equal to 120 cm³. Proceeding from these data, height of a pyramid is so: h = 3*120/46 = 7.83 smotvt: height of this pyramid will be, about, 7.83 smprimer 2: At a pyramid in which basis the regular polygon - a square lies its diagonal is equal to 14 cm, length of an edge is 15 cm. According to these data to find pyramid height, it is required to use the following formula (which appeared as a result from Pythagorean theorem): h² = 15² - 14²h² = 225 - 196 = 29h = √29 smotvt: height of this pyramid is √29 cm or, about, 5.4 cm