At the base of the straight prism ABCA1B1C1 lies a triangle ABC, in which the angle C = 90 degrees

At the base of the straight prism ABCA1B1C1 lies a triangle ABC, in which the angle C = 90 degrees, the angle B = 30 degrees, AB = 4cm. Find the volume of the prism if the angle BAB1 = 45 degrees.

In a right-angled triangle ABC, the leg AC lies opposite the angle 30, then AC = AB / 2 = 4/2 = 2 cm.Then BC ^ 2 = AB ^ 2 – AC ^ 2 = 16 – 4 = 12.

BC = 2 * √3 cm.

Determine the area of the base of the prism.

Sbn = ВС * АС / 2 = 2 * 2 √3 / 2 = 2 * √3 cm2.

Since the prism is straight, the triangle ABB1 is rectangular, and since the angle BAB1 = 45, the legs of this triangle are equal, AB = BB1 = 4 cm.

Let’s define the volume of the prism.

V = S main * BB1 = 2 * √3 * 4 = 8 * √3 cm3.

Answer: The volume of the prism is 8 * √3 cm3.