The height of a regular triangular pyramid is 10 dm. The lateral rib is inclined to the base plane at an angle

| August 11, 2021 | education

The height of a regular triangular pyramid is 10 dm. The lateral rib is inclined to the base plane at an angle of 45 degrees – calculate the perimeter of the base of the pyramid.

In a right-angled triangle AOD, one of the acute angles is 450, then such a triangle is isosceles and the lengths of its legs are equal. AO = DO = 10 dm.

Since the pyramid is regular, there is an equilateral triangle ABC at its base, and then the segment AO is the radius of the circle circumscribed around the triangle. Then AO = a / √3, where a is the side of a regular triangle. a = BC = AB = AC = AO * √3 = 10 * √3 dm.

Then the perimeter of the base of the pyramid is: Ravsd = 3 * AB = 3 * 10 * √3 = 30 * √3 cm.

Answer: The perimeter of the base of the pyramid is 30 * √3 cm.



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.