Question

Обьем правильной треугольной пирамиды ровен 144 см3, а её боковой кант наклонен к плоскости основы под углом 45. Вычислите площадь боковой поверхности пирамиды. Помогите народ!!!

Answer 1

V= 1/3Sосн.* H
Sбок.= Sосн*Н, получается что площадь в 3 раза больше объма, = 144*3=423см²

Answer 2

Calculating the Surface Area of a Triangular Pyramid

To calculate the surface area of a triangular pyramid, we need to use the formula:

Surface Area = 0.5 * Perimeter of Base * Slant Height + Area of Base

First, let's calculate the slant height of the pyramid using the given information.

The volume of the pyramid is given as 144 cm^3, and the slant height is inclined at an angle of 45 degrees to the base. We can use this information to calculate the slant height.

Calculating the Slant Height

The formula for the volume of a pyramid is given by: Volume = (1/3) * Area of Base * Height

Given that the volume is 144 cm^3, we can rearrange the formula to solve for the height: Height = (3 * Volume) / Area of Base

Calculating the Area of the Base

The area of the base of a triangular pyramid can be calculated using the formula: Area of Base = (Base Perimeter * Apothem) / 2

Calculating the Perimeter of the Base

The perimeter of the base can be calculated by adding the lengths of all the sides of the base triangle.

After calculating the slant height and the area of the base, we can use these values to find the surface area of the pyramid.

Let's proceed with these calculations.