Question

высота правильной четырёхугольгой пирамиды равна 3, а апофема пирамиды равна 5 Найти сторону основания пирамиды​

Answer 1

Finding the Side Length of a Pyramid's Base

To find the side length of the base of a pyramid, we can use the given information about the height and apothem of the pyramid.

Given: - Height of the pyramid = 3 - Apothem of the pyramid = 5

We need to find the side length of the base of the pyramid.

To solve this, we can use the formula for the slant height of a pyramid, which is given by:

Slant Height (l) = sqrt(height^2 + apothem^2)

Substituting the given values, we have:

l = sqrt(3^2 + 5^2) = sqrt(9 + 25) = sqrt(34)

Now, we can use the slant height and the apothem to find the side length of the base of the pyramid using the formula:

Side Length (s) = 2 * apothem * tan(180 / n)

where n is the number of sides of the base of the pyramid.

Since the pyramid is a four-sided pyramid (a tetrahedron), n = 4.

Substituting the values, we have:

s = 2 * 5 * tan(180 / 4) = 10 * tan(45) = 10

Therefore, the side length of the base of the pyramid is 10.

Please note that the calculations are based on the given information and the formulas for pyramid geometry.