Question

Диагональ правильной четырехугольной призмы равна 10см и образует с боковой гранью угол 30°. Найдите площадь основания призмы

Answer 1

Решение:
1)√(100 -25)= √75 =5√3
2)h² =(5√3)² -5² =√50=5√2
3)4*5*5√2=100√2
4)2*5*5=50 см²
Ответ. 50см²

Answer 2

Finding the Base Area of a Prism

To find the base area of a prism, we need to know the diagonal length of the prism's base and the angle it forms with one of the lateral faces.

In this case, we are given that the diagonal length of the base of a four-sided prism is 10 cm, and it forms a 30° angle with one of the lateral faces.

To calculate the base area, we can use trigonometry and the given information.

Let's denote the length of one side of the base as s. Since the base is a four-sided figure, all sides are equal.

Using trigonometry, we can determine that the length of one side of the base is given by s = 10 cm * sin(30°).

Now, to find the base area, we need to calculate the area of a square with side length s.

The formula for the area of a square is A = s^2.

Let's calculate the base area step by step:

1. Calculate the length of one side of the base: - s = 10 cm * sin(30°). - Using a calculator, we find that s ≈ 5 cm.

2. Calculate the base area: - A = s^2. - A = (5 cm)^2. - A = 25 cm^2.

Therefore, the base area of the given prism is approximately 25 cm^2.

Please note that the calculations provided above are based on the given information and assumptions about the shape of the prism. If there are any additional details or constraints, please let me know, and I'll be happy to assist you further.