How to find the right height in the pyramid
The pyramid is a polyhedron, which lies at the base of the polygon and its faces are triangles having a common vertex. For regular pyramid same definition is valid, but it lies at the base of a regular polygon. By the height of the pyramid is meant a segment which is held from the top to the bottom of the pyramid, and this segment is perpendicular to it. Find the correct height in the pyramid is very easy.
You will need:
Depending on the situation, to know the volume of the pyramid, square pyramid side faces, edges, a length, the length of the polygon diameter at the bottom.
Instruction how to find the right height in the pyramid
One way to find the height of the pyramid, and not just the right - this is to express it in terms of the volume of the pyramid. The formula by which you can see its volume looks like: V = (S * h) / 3, where S - area of the side faces of the pyramid in the amount, h - the height of the pyramid. Then from this formula can be derived other, to find the height of the pyramid: h = (3 * V) / S, for example, it is known that the area of the side faces of the pyramid 84 cm², and the volume of the pyramid is 336 cc Then you can find the height: h = (3 * 336) / 84 = 12 cm Answer: The height of the pyramid of 12 cm
Considering the regular pyramid whose base is a regular polygon, we can conclude that the triangle formed by the height, half diagonally and one of the faces of the pyramid, is a right-angled triangle (eg, triangle AEG is the figure above). According to the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the legs (a² = b² + c²). In the case of the right pyramid hypotenuse - this side of the pyramid, one of the legs - half of the diagonal of the polygon in the base and the other leg - the height of the pyramid. In this case, knowing the length of the sides and diagonals can be computed and height. As an example, consider the triangle AEG: AE² = EG² + GA² Hence GA pyramid height can be expressed as follows: GA = √ (AE²-EG²).
To clarify how to find the correct height of the pyramid, we can consider an example: the correct length of the pyramid faces 12 cm, length of the diagonal of the polygon at the base - 8 cm From these data, it is required to find the length of the height piramidy.Reshenie:. 12² = 4² + c², where c - the unknown leg (height) of the pyramid (right triangle). 16 + 144 = 128 Thus, the height of the pyramid √128 or approximately 11.3 cm