Given a regular triangular pyramid, the side of the base is 4 cm, the side edge forms an angle

| June 17, 2021 | education

Given a regular triangular pyramid, the side of the base is 4 cm, the side edge forms an angle of 45 degrees with its base, find the volume.

In an equilateral triangle ABC, draw the height AH and determine its length.

AH = a * √3 / 2, where a is the length of the side of the triangle. AH = 4 * √3 / 2 = 2 * √3 cm.

Determine the area of the base of the pyramid. Sbn = ВС * АН / 2 = 4 * 2 * √3 / 2 = 4 * √3 cm2.

The segment AO is the radius of a circle circumscribed around the triangle ABC, then AO = BC / √3 = 4 / √3 cm.

The DAO triangle is rectangular and isosceles, since its angle A is 45, then DO = AO = 4 / √3 cm.

Let’s define the volume of the pyramid.

V = Sbase * DO / 3 = (4 * √3 * 4 / √3) / 3 = 16/3 = 5 (1/3) cm3.

Answer: The volume of the pyramid is 5 (1/3) cm3.



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.