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

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.