The base of a straight prism is a right-angled triangle with 5 and 12 cm legs.

| March 15, 2021 | education

The base of a straight prism is a right-angled triangle with 5 and 12 cm legs. Find the area of the lateral surface of the prism if its largest lateral edge is a square.

According to the condition of the problem, the base of the straight prism is a right-angled triangle, the legs of which are known.

Using the Pythagorean theorem, we find the third side of this triangle, denoting it with the letter x.

х² = 5² + 12²,

x² = 25 + 144,

x² = 169,

x = 13 (cm).

This side of the triangle is its large side, and therefore the side of the larger face of the prism.

Since the large face of the prism is a square, it means that the height of the prism is equal to the larger side of the base, that is, equal to 13 cm.

Thus, the area of the lateral surface of the prism is:

S = 13 * (5 + 12 + 13) = 13 * 30 = 390 (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.