In the regular triangular pyramid SABC, point Q is the midpoint of edge AB, S

In the regular triangular pyramid SABC, point Q is the midpoint of edge AB, S is the vertex. It is known that BC = 5 and the lateral surface area is 45. Find the length of the segment SQ

Since the trapezoid is regular, the triangle ABC at its base is isosceles, AB = BC = AC = 5 cm.

Since point Q is the midpoint of side AB, the segment SQ is the median of triangle SAB, and since triangle SAB is isosceles, SQ is also the height of this triangle.

Since the areas of the side faces of the regular pyramid are equal, then Ssa = S side / 3 = 45/3 = 15 cm2.

… Ssa = AB * SQ / 2.

SQ = 2 * Ssaв / AB = 2 * 15/5 = 6 cm.

Answer: The length of the segment SQ is 6 cm.