Question

В основании прямой призмы лежит параллелограмм со сторонами 2см и 3см и острым углом 30 градусов. Высота призмы 4см. Найти объем призмы.

Answer 1

Всё подробно написала в решении......

Answer 2

Calculation of the Prism Volume

To find the volume of a prism, we need to multiply the area of the base by the height of the prism. In this case, the base of the prism is a parallelogram with sides measuring 2 cm and 3 cm, and an acute angle of 30 degrees. The height of the prism is 4 cm.

To calculate the area of the base, we can use the formula for the area of a parallelogram: Area = base * height. In this case, the base is the side length of the parallelogram, which is 2 cm, and the height is the perpendicular distance between the base and the opposite side, which can be calculated using trigonometry.

Let's calculate the area of the base first:

Base = 2 cm

Height = 3 cm * sin(30 degrees) = 3 cm * 0.5 = 1.5 cm

Area = Base * Height = 2 cm * 1.5 cm = 3 cm^2

Now that we have the area of the base, we can calculate the volume of the prism:

Volume = Area of Base * Height of Prism = 3 cm^2 * 4 cm = 12 cm^3

Therefore, the volume of the prism is 12 cubic centimeters.