The base of the straight prism is a triangle with sides of 8 cm and 15 cm and the angle between them is 60 degrees.

The base of the straight prism is a triangle with sides of 8 cm and 15 cm and the angle between them is 60 degrees. The height of the prism is 11 cm. Find the lateral area and the total surface area of the prism.

1) S side surface = P base * height.
Find P of the base.
P base is equal to the sum of all sides. But we are missing the meaning of one side. Let’s find it through the cosine theorem:
a ^ 2 = 8 ^ 2 + 15 ^ 2-2 * 8 * 15 * cos60 = 64 + 225-2 * 8 * 15 * 0.5 = 289-120 = 169
a = 13
Hence, the third side is 13. Now we find the P base:
P = 13 + 15 + 8 = 36
S lateral surface area = 36 * 11 = 396
2) S full surface = S side p. + 2 * S base
S base = (8 * 15 * sin60) / 2 = 30√3
S full surface = 396 + 2 * 30√3 = 396 + 60√3