Question

Знайдіть об'єм прямої призми, в основі якої лежить трикутник зі сторонами 2 см і 6 см і кутом між ними, що становить 30°, якщо висота призми дорівнює 5 см.​

Answer 1

Ответ:

15см³

Дано:

ABCA1B1C1-Прямая призма.

∆ABC-основание;

АС=2см;

АВ=6см

∠САВ=30°

АА1=5см

___________

Решение:

Sосн=½*АС*АВ*sin∠А;

sin30°=½

Sосн=½*2*6*½=3см²

V=Sосн*АА1=3*5=15см³

Answer 2

Calculating the Volume of a Prism

To calculate the volume of a prism, we can use the formula:

Volume = Area of Base x Height

In this case, the base of the prism is a triangle with sides of 2 cm and 6 cm and an included angle of 30°, and the height of the prism is 5 cm.

Finding the Area of the Base Triangle

To find the area of the base triangle, we can use the formula for the area of a triangle:

Area = (1/2) x base x height x sin(angle)

Substituting the given values: - Base = 6 cm - Height = 2 cm - Angle = 30°

We can calculate the area of the base triangle using the given formula.

Calculating the Volume

Once we have the area of the base triangle, we can use it to calculate the volume of the prism using the formula:

Volume = Area of Base x Height

Substitute the calculated area of the base triangle and the given height to find the volume of the prism.

Let's calculate the area of the base triangle and then use it to find the volume of the prism.