In the regular triangular pyramid SABC M is the midpoint of the edge AB S is the vertex. It is known that BC

In the regular triangular pyramid SABC M is the midpoint of the edge AB S is the vertex. It is known that BC = 4 and the area of the side surface of the pyramid is 18. Find the length of the segment SM.

Since the pyramid is regular, a regular triangle lies at its base, and the areas of its side faces are equal.

Then the area of one side face of SAB will be equal to: Ssav = Spir / 3 = 18/3 = 6 cm2.

The side faces are isosceles triangles. Since point M is the midpoint of side AB, segment SM is the median of triangle SAB, and since it is isosceles, then its height.

Then Ssav = AB * SM / 2.

SM = 2 * Ssav / AB.

Since triangle ABC is correct, AB = BC = 4 cm.

Then: SM = 2 * 6/4 = 3 cm.

Answer: The length of the segment SM is 3 cm.