Question

в правильной четырехугольной усеченной пирамиде высота равна 36 см,апофема равна 45 см,а стороны основания относятся как 1:4,найти эти стороны

Answer 1

использовано определение правильной 4-хугольной усеченной пирамиды, теорема Пифагора

Answer 2

Given Information:

We are given the following information about a truncated pyramid: - Height of the pyramid (h) = 36 cm - Apothem (a) = 45 cm - The sides of the base are in a ratio of 1:4

Solution:

To find the lengths of the sides of the base, we can use the given ratio. Let's assume the length of the shorter side is x, and the length of the longer side is 4x.

We can use the Pythagorean theorem to relate the height, apothem, and the lengths of the sides of the base. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the height (h) is the hypotenuse, and the apothem (a) and the shorter side (x) are the other two sides of the right triangle.

Using the Pythagorean theorem, we have:

x^2 + a^2 = h^2

Substituting the given values, we get:

x^2 + 45^2 = 36^2

Simplifying the equation:

x^2 + 2025 = 1296

x^2 = 1296 - 2025

x^2 = -729

Since the square of a real number cannot be negative, this equation has no real solutions. Therefore, there is no valid solution for the lengths of the sides of the base of the truncated pyramid given the provided information.

Please note that the given information may be incorrect or incomplete, as the equation does not yield real solutions.

Let me know if there's anything else I can help you with!