Question

в правильной четырехугольной пирамиде сторона основания равна 6 площадь боковой поверхности в два раза больше площади основания найти объем пирамиды и площадь боковой поверхности помогите пожалуста и быстрее!!

Answer 1

Sосн=6^2=36

Sб=36*2=72

Sтр=72/4=18

S=6*h*1/2=18

h=6

H^2=6^2-3^2=36-9=27

H=3sqrt(3)

V=36*3sqrt(3)/3=36sqrt(3)

Answer 2

Given Information:

We are given that the side length of the base of a right quadrilateral pyramid is 6, and the lateral surface area is twice the area of the base. We need to find the volume of the pyramid and the lateral surface area.

Finding the Lateral Surface Area:

To find the lateral surface area of a pyramid, we need to know the slant height. However, the slant height is not given in the question. Therefore, we cannot directly calculate the lateral surface area.

Finding the Volume:

The volume of a pyramid can be calculated using the formula: Volume = (1/3) * base area * height.

To find the height of the pyramid, we can use the Pythagorean theorem. Let's consider the right triangle formed by the height, half the base, and the slant height. The Pythagorean theorem states that the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides.

Let's assume the slant height is 's'. Then, we have: s^2 = (6/2)^2 + h^2 s^2 = 9 + h^2

Since we know that the lateral surface area is twice the area of the base, we can write: 2 * base area = lateral surface area

The base of the pyramid is a quadrilateral, and we are not given any specific information about its shape. Therefore, we cannot calculate the base area.

In conclusion, without the slant height or the base area, we cannot calculate the volume or the lateral surface area of the pyramid.