Calculate the volume of the prism, the base is a parallelogram with sides of 8 and 6 cm and a cut of 30 °

Calculate the volume of the prism, the base is a parallelogram with sides of 8 and 6 cm and a cut of 30 °, and the height of the prism = 7 cm.

The volume of the prism can be calculated using the formula:

V = S * h, where S is the area of the base of the prism, h is the height of the prism (h = 7 cm).

At the base of the prism lies a parallelogram whose area is equal to:

S = a * b * sinα, where a is the large side of the parallelogram (a = 8 cm), b is the smaller side of the parallelogram (b = 6 cm), α is the angle between sides a and b (α = 30º).

Let’s calculate the volume of the prism:

V = S * h = a * b * sinα * h = 8 * 6 * sin30º * 7 = 8 * 6 * 0.5 * 7 = 168 cm3.

Answer: The volume of the prism is 168 cm3.