Question

Дана правильная треугольная пирамида. сторона основания a и высота пирамиды h. найдите объем пирамиды

Answer 1

V = ha² / (4√3)
Формула для правильной пирамиды такая есть, так что просто её написать и все.

Answer 2

Calculating the Volume of a Triangular Pyramid

To find the volume of a triangular pyramid with a base side length of *a* and a height of *h*, you can use the formula:

V = (1/3) * (Area of Base) * (Height)

Where the area of the base can be calculated using the formula for the area of a triangle:

Area of Base = (1/2) * a * h

Applying the Formula

Using the given values of the base side length *a* and the height *h*, we can calculate the volume of the pyramid:

V = (1/3) * (1/2 * a * h) * h

Calculating the Volume

Substitute the given values of *a* and *h* into the formula:

V = (1/3) * (1/2 * a * h) * h

V = (1/6) * a * h^2

So, the volume of the triangular pyramid is (1/6) * a * h^2.