Find the volume of a prism, the base of which is a parallelogram with sides of 2 cm and 3 cm and an angle

Find the volume of a prism, the base of which is a parallelogram with sides of 2 cm and 3 cm and an angle of 45 ° between them, if the height of the prism is 2√2 cm.

The volume of the prism is equal to the product of the area of its base by the height:

V = S main * h.

At the base of this prism lies a parallelogram, its area can be defined as the product of the lengths of two adjacent sides by the sine of the angle between them:

Sb = a * b * sin α = 2 * 3 * sin 45 ° = 2 * 3 * √2 / 2 = 3√2 cm2.

Knowing the base area and height, we find the volume:

V = Sb * h = 3√2 * 2√2 = 3 * 2 * 2 = 12 cm3.