Question

Площадь полной поверхности правильного четырёхугольной пирамиды равно 144, а сторона основания равно 8. Найдите длину высоты этой пирамиды.С решением пожалуйста.

Answer 1

Площадь полной поверхности прав.4ёх-угольной пирамиды находится по формуле:   4*(площадь бок.пов.)+площадь основания..затем подставляем все известное в формулу,получаем:
144=4*(1/2*8*SH)+64,где SH-высота бок.грани
144=16SH+64
144-64=16SH
80=16SH
SH=5
затем,находим SO(высота самой пирамиды):
по т.пифагора:
25-16=9,следовательно высота пирамиды равна 3

Answer 2

Вот. Что не понятно - поясню

Answer 3

Calculation of the Height of the Pyramid

To find the height of the pyramid, we can use the formula for the surface area of a regular quadrilateral pyramid and the given information about the surface area and the side length of the base.

The formula for the surface area of a regular quadrilateral pyramid is:

Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height

Given: - Surface Area = 144 - Side Length of Base = 8

Let's calculate the height of the pyramid using this information.

1. Calculate the Base Area: The base of the pyramid is a square, so the area of the base is equal to the side length squared. Base Area = Side Length of Base * Side Length of Base = 8 * 8 = 64.

2. Calculate the Perimeter of the Base: The perimeter of the base of a square is equal to 4 times the side length. Perimeter of Base = 4 * Side Length of Base = 4 * 8 = 32.

3. Substitute the values into the formula for Surface Area: 144 = 64 + (1/2) * 32 * Slant Height.

4. Simplify the equation: 144 = 64 + 16 * Slant Height.

5. Subtract 64 from both sides of the equation: 80 = 16 * Slant Height.

6. Divide both sides of the equation by 16: Slant Height = 80 / 16 = 5.

Therefore, the length of the slant height of the pyramid is 5.

To find the height of the pyramid, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.

Let's calculate the height of the pyramid using the slant height and the side length of the base.

1. Calculate the length of the height: Using the Pythagorean theorem, we have: Height^2 = Slant Height^2 - (Side Length of Base / 2)^2.

Plugging in the values: Height^2 = 5^2 - (8 / 2)^2 = 25 - 16 = 9.

2. Take the square root of both sides of the equation: Height = √9 = 3.

Therefore, the length of the height of the pyramid is 3.

So, the length of the height of the given pyramid is 3.