Question

Большая диагональ правильной шестиугольной призмы равна 20в корне из 2 см и наклонена к плоскости основания под углом 45 градусов. Вычислите площади боковой и полной поверхности призмы.

Answer 1

Решение дано на фото.

Answer 2

Calculating the Surface Areas of a Prism

To calculate the surface areas of the given hexagonal prism, we can use the following formulae:

1. Lateral Surface Area (A_l): - The lateral surface area of a prism can be calculated using the formula: A_l = perimeter of base * height - For a regular hexagon, the perimeter can be calculated as 6 * side length.

2. Total Surface Area (A_t): - The total surface area of the prism includes the lateral surface area and the areas of the two bases.

Given Information

- Diagonal of the hexagonal prism: 20√2 cm - Angle of inclination to the base: 45 degrees

Calculating the Side Length of the Hexagon

To calculate the side length of the hexagon, we can use the formula for the diagonal of a regular hexagon: - Diagonal (d) = √3 * side length - Given diagonal = 20√2 cm

Solving for the side length: - 20√2 = √3 * side length - side length = 20√2 / √3 - side length ≈ 12.247 cm

Calculating the Lateral Surface Area (A_l)

The lateral surface area of the hexagonal prism can be calculated using the formula: - A_l = perimeter of base * height - For a regular hexagon, the perimeter can be calculated as 6 * side length.

Substituting the values: - A_l = 6 * 12.247 cm * height

Calculating the Total Surface Area (A_t)

The total surface area of the hexagonal prism can be calculated using the formula: - A_t = A_l + 2 * base area

The base area of a regular hexagon can be calculated using the formula: - Base area = (3√3 / 2) * side length^2

Substituting the values: - Base area = (3√3 / 2) * (12.247 cm)^2

Now, we can calculate the total surface area using the lateral surface area and the base area.

Please note that the exact value of the height is not provided, so the final numerical value of the lateral surface area and total surface area cannot be calculated without the height of the prism.