SABC – regular triangular pyramid, base side = 6 cm.Side. = 63 cm2. Find apothem.

Since the SABC pyramid is regular, its lateral faces are isosceles equal triangles.

Then Ssbc = S side / 3 = 63/3 = 21 cm2.

Let us construct the height SH in the triangle SBC, which will be the desired apothem of the pyramid.

Then Ssbc = BC * SH / 2.

SH = 2 * Ssbc / BC = 2 * 21/6 = 7 cm.

Answer: The apothem of the pyramid is 7 cm.

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