# In a regular triangular pyramid SABC, Q is the middle of the edge AB, S is the apex.

In a regular triangular pyramid SABC, Q is the middle of the edge AB, S is the apex. It is known that SQ = 28, and the lateral surface area is 294. Find the length of the segment BC.

Since point M is the midpoint of the edge BC, the segment SQ is the median of the side face SBC. Since the side face of a regular pyramid is an equilateral triangle, the median SQ is also its height.

The side faces of the regular pyramid are equal, then Sside = 3 * Ssвс.

Ssvs = 294/3 = 98 cm2.

The area of the side facet SBC is equal to: Ssвс = BC * SQ / 2 = 98.

ВС = Ssвс * 2 / SQ = 98 * 2/28 = 7 cm

Answer: The length of the BC segment is 7 cm.

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