Question

Площадь полной поверхности правильной треугольной пирамиды в 7 раз больше площади ее основания . во сколько раз площадь полной поверхности этой пирамиды больше площади боковой грани?

Answer 1

Площадь боковой поверхности правильной усечённой пирамиды равна полупроизведению суммы периметров её оснований и апофемы
Элементарно :)
((9+33)*5) :2=105см в квадрате

Answer 2

Calculation of Surface Area

To find the ratio of the surface area of a regular triangular pyramid to the area of its base, we need to know the relationship between the surface area and the base area of a regular triangular pyramid.

Let's assume that the base area of the pyramid is A. According to the given information, the total surface area of the pyramid is 7 times larger than the base area. Therefore, the total surface area can be expressed as 7A.

To find the ratio of the total surface area to the area of a lateral face (the side face of the pyramid), we need to subtract the area of the base from the total surface area. The lateral faces of a regular triangular pyramid are congruent equilateral triangles.

Calculation of Lateral Face Area

The area of an equilateral triangle can be calculated using the formula:

Area = (sqrt(3) / 4) * s^2

Where s is the length of one side of the equilateral triangle.

In a regular triangular pyramid, the base is also an equilateral triangle. Therefore, the area of the base can be calculated using the same formula.

Now, let's calculate the ratio of the total surface area to the area of a lateral face.

Calculation Steps:

1. Calculate the area of the base (A) using the given information. 2. Calculate the total surface area (7A) using the given information. 3. Calculate the area of a lateral face (L) using the formula for the area of an equilateral triangle. 4. Calculate the ratio of the total surface area to the area of a lateral face (7A / L).

Calculation:

1. Let's assume the area of the base is A. 2. According to the given information, the total surface area is 7 times larger than the base area: Total Surface Area = 7A. 3. The area of an equilateral triangle (the lateral face) can be calculated using the formula: Lateral Face Area = (sqrt(3) / 4) * s^2, where s is the length of one side of the equilateral triangle. 4. The ratio of the total surface area to the area of a lateral face is: Ratio = Total Surface Area / Lateral Face Area.

Let's calculate the values step by step.

1. Calculation of the area of the base (A): - Unfortunately, we don't have the specific value for the area of the base. Without this information, we cannot calculate the exact values for the total surface area and the area of a lateral face.

Note: To provide a more accurate answer, we would need the specific value for the area of the base.

2. Calculation of the total surface area (7A): - Since we don't have the specific value for the area of the base, we cannot calculate the exact value for the total surface area.

3. Calculation of the area of a lateral face (L): - Without the specific value for the area of the base, we cannot calculate the exact value for the area of a lateral face.

4. Calculation of the ratio of the total surface area to the area of a lateral face (7A / L): - Without the specific values for the total surface area and the area of a lateral face, we cannot calculate the exact ratio.

Unfortunately, without the specific value for the area of the base, we cannot provide the exact ratio of the total surface area to the area of a lateral face for the given pyramid.

If you have any other questions, feel free to ask!