In the regular pyramid SABC, R is the midpoint of the edge BC, S is the vertex. It is known that AB = 8, and the lateral surface area is 252. Find the length of the segment SR.
Since the pyramid is regular, a regular triangle lies at its base, and the areas of its lateral faces are equal.
Then the area of one side face of SAB will be equal to: Ssav = Spir / 3 = 252/3 = 84 cm2.
The side faces are isosceles triangles. Since point R is the midpoint of side BC, then segment SR is the median of triangle SBC, and since it is isosceles, then its height.
Then Ssвс = ВС * SR / 2.
SR = 2 * Ssbc / BC.
Since the triangle ABC is correct, then AB = BC = 8 cm.
Then: SM = 2 * 84/8 = 21 cm.
Answer: The length of the SR segment is 21 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.