You will need
- Pen, paper, calculator
In this case, the edges of the pyramid are the sides of these equilateral triangles. The altitude of the right triangular pyramid is the length of the edge of the pyramid, multiplied by the square root of two thirds : h=√2/3.
To calculate the height of every other triangular pyramid we can use the formula volume V = 1/3Sh, where V is the volume of a pyramid, S is the area of the base, and h is the height. From the formula of the volume derive the formula for the height: to find the altitude of a triangular pyramid, multiply the volume of the pyramid by 3 and divide the resulting value by the area of the base: h=3V/S.
Since the base of a triangular pyramid is a triangle, use the formula for calculating the area of the triangle. If you know the length of one side of the triangle (a) and height (h) is omitted on this side, then calculate the area by multiplying the length of the side length of the height and dividing the resulting value by 2: S=1/2ah. If you know two sides of a triangle (a and b) and the angle between them (C), use the formula: S=1/2absinC. The value of the sine of the angle can be viewed in the table of sines, which is easy to find online.
Typically, if the problem is to find the height of a triangular pyramid, the volume of this pyramid are known. Therefore, having found the area of the base of the pyramid, it remains only to multiply the volume by 3 and divided by the area of the base to get the height of a triangular pyramid.
Do not confuse the height of the pyramid which is perpendicular to the plane of its base, with apofema, which is the height of the side faces.