# 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

Step 1:

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

Step 2:

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).

Step 3:

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