The base of a straight prism is a rhombus with an acute angle of 30 degrees. The lateral surface of the prism is 96 dm2

| May 21, 2021 | education

The base of a straight prism is a rhombus with an acute angle of 30 degrees. The lateral surface of the prism is 96 dm2, and the total surface is 132. Find the height of the prism.

The total surface area of the prism is the sum of the lateral surface areas and the two bases:

S full = S side + 2 * S main.

Hence, Sbn = (Sful – Side) / 2 = (132 – 96) / 2 = 36/2 = 18 dm2.

At the base of this prism is a rhombus, its area is defined as the product of the square of the side by the sine of the angle between the sides:

Sbn = a2 * sin 30 °.

We can find the side of the rhombus:

a2 = Sb / sin 30 ° = 18 / 0.5 = 36;

a = √36 = 6 dm.

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

Sside = P * h = 4 * a * h.

Let’s find the required height of the prism:

h = S side / P = 96/24 = 4 dm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.