Question

Ребят,помогите, после сотрясения мозга ничего понять не могу: В правильной четырехугольной пирамиде SABD т.О-центр основания,S-вершина,SO=8 BD=30.Найти боковое ребро SC

Answer 1

АВСД - основание в правильной четырехугольной пирамиде  - квадрат

тогда ВД - диагональ основания

SO  - высота пирамиды, точка о находит в точке пересечения диагоналей.

если взять половину диагонали то получится прямоугольный треугольник  с катетом SO и BD/2 , отсюда по теореме пифагора найдем ребро:

x² = 64 + 225 = 289

x = 17 = SC

 

 

Answer 2

Problem Analysis

We are given a regular quadrilateral pyramid SABD, where O is the center of the base, S is the apex, and SO = 8 and BD = 30. We need to find the length of the lateral edge SC.

Solution

To find the length of the lateral edge SC, we can use the Pythagorean theorem. The lateral edge SC is the hypotenuse of a right triangle with sides SO and OC, where OC is the height of the pyramid.

Let's denote the length of the lateral edge SC as x. We can set up the following equation using the Pythagorean theorem:

SC^2 = SO^2 + OC^2

Since the pyramid is regular, the height OC is perpendicular to the base SABD and passes through the center O. Therefore, OC is the height of an equilateral triangle with side length BD.

To find the height of the equilateral triangle, we can use the formula:

OC = BD * sqrt(3) / 2

Substituting the given values, we have:

OC = 30 * sqrt(3) / 2

Now, we can substitute the values of SO and OC into the equation for SC^2:

SC^2 = 8^2 + (30 * sqrt(3) / 2)^2

Simplifying the equation, we get:

SC^2 = 64 + 900 * 3 / 4

SC^2 = 64 + 2700 / 4

SC^2 = 64 + 675

SC^2 = 739

Taking the square root of both sides, we find:

SC = sqrt(739)

Therefore, the length of the lateral edge SC is approximately 27.18.

Answer

The length of the lateral edge SC in the given regular quadrilateral pyramid SABD is approximately 27.18.