In a regular triangular prism, the diagonal of the side face is 25 cm, and the height is 20 cm.

univerkov | August 4, 2021 | education

In a regular triangular prism, the diagonal of the side face is 25 cm, and the height is 20 cm. Find the area of the lateral surface of the prism.

The side faces of the prism are three equal rectangles. The diagonal CB1 of the side face forms a right-angled triangle CC1B1 from which, according to the Pythagorean theorem, we determine the length of the side of the base. CC1 ^ 2 = AB1 ^ 2 – BC ^ 2 = 25 ^ 2 – 20 ^ 2 = 625 – 400 = 225.

CC1 = 15 cm.

Determine the perimeter of the triangle at the base of the prism.

Rosn = 3 * CC1 = 3 * 15 = 45 cm.

Then S side = Ron * CC1 = 45 * 20 = 900 cm2.

Answer: The lateral surface area is 900 cm2.

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.