The pyramid in which basis the triangle lies is called triangular. The perpendicular lowered from top on the plane of its basis will be height of such pyramid. To find height of the regular triangular pyramid, that is such pyramid which all sides are equilateral triangles it is necessary to know pyramid edge length (a).
It is required to you
- Handle, paper, calculator
Instruction
1. In this case the parties of these equilateral triangles will be edges of a pyramid. The pyramid edge length multiplied by a root from two thirds will be height of the regular triangular pyramid: h= a2/3.
2. For calculation of height of any other triangular pyramid it is possible to use a volume formula: V = 1/3Sh where V is a volume of a pyramid, S is the area of the basis, and h is height. We bring height formula out of a formula of volume: to find height of a triangular pyramid, it is necessary to increase pyramid volume by 3 and to divide the received value into the area of the basis: h=3V/S.
3. As the triangle forms the basis of a triangular pyramid, we will use a formula of calculation of the area of a triangle. If length of one party of this triangle (a) and height (h) lowered on this party is known, then we count the area, having increased length of the party by length of height and having divided the received value into 2: S=1/2ah. If two parties of a triangle are known (an and b) and a corner between them (C), we use a formula: S=1/2absinC. It is possible to look at value of a sine of the angle in the table of sine which is easy for finding in the Internet.
4. As a rule, if it is required to find height of a triangular pyramid in a task, the volume of this pyramid is known. Therefore after the area of the basis of a pyramid is found, it is necessary only to increase volume by 3 and to divide into the area of the basis to receive height of a triangular pyramid.