How To Find The Height Of A Triangular Pyramid | The Science

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# How to find the height of a triangular pyramid

It called triangular pyramid whose base is a triangle. The height of the pyramid is the perpendicular dropped from the vertex to its base plane. To find the height of a regular triangular pyramid, that is, a pyramid whose faces are all equilateral triangles, you need to know the length of the edges of the pyramid (a).

### You will need:

Pen, paper, calculator

## Instruction how to find the height of a triangular pyramid

Step 1:

In this case, the side edges of the pyramids are equilateral triangles. The height of a regular triangular pyramid is the length of the edges of the pyramid, multiplied by the square root of two-thirds: h = a√2 / 3.

Step 2:

To calculate the height of any other triangular pyramid, you can use the volume formula: V = 1 / 3Sh, where V - is the volume of the pyramid, S - is the area of ​​the base and h - is the height. From the formula we derive the formula volume height: to find the height of a triangular pyramid, multiply the volume of the pyramid 3 and divide this value by the area of ​​the base: h = 3V / S.

Step 3:

Since the base of a triangular pyramid is a triangle, use the formula for calculating the area of ​​a triangle. If you know the length of one side of the triangle (a) and height (h), let down on this side, the forward area by multiplying the length of the side at the height of the length and dividing the result by 2: S = 1 / 2ah. If the two sides of the triangle are known (a and b) and the angle between them (C), then use the formula: S = 1 / 2absinC. The value of the sine of the angle you can see in the table of sines, which is easy to find on the Internet.

Step 4:

Typically, if a problem is to find the height of a triangular pyramid, the pyramid is known volume. Therefore, after the base area of ​​the pyramid is found, the volume can only multiply and divide by 3 for the base area to a height of a triangular pyramid.