# In the regular quadrangular pyramid SABCD, the point is O-center of the base, S apex, SB

In the regular quadrangular pyramid SABCD, the point is O-center of the base, S apex, SB = 17, BD = 30. Find the length of the segment SO.

Since the pyramid is regular, there is a square at its base, and the vertex S is projected to the point of intersection of the diagonals.

The diagonals of the square are equal and are halved at the intersection. Then BO = OS = BD / 2 = 30/2 = 15 cm.

In the right-angled triangle SBO, by the Pythagorean theorem, we define the leg SO, which is the height of the pyramid.

SO ^ 2 = SB ^ 2 – BO ^ 2 = 289 – 225 = 64.

SO = 8 cm

Answer: The length of the SO segment is 8 cm.

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