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

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

According to the cosine theorem, the square of the side of a triangle is equal to the sum of the squares of the other two sides minus their double product by the cosine of the angle between them. Find the third side of the base of this triangular prism:

c = a ^ 2 + b ^ 2 – 2 * a * b * cos α = 8 ^ 2 + 15 ^ 2 – 2 * 8 * 15 * cos 60 ° = 64 + 225 – 120 = 169 = 132;

c = 13 cm.

The area of the lateral surface of a straight prism is equal to the product of the perimeter of the base of the prism by its height:

Sside = P * h = (8 + 15 + 13) * 11 = 36 * 11 = 396 cm2.