In the regular quadrangular pyramid Sabcd, point O is the center of the base, SB = 20, AC = 24.
| March 23, 2021 | education
In the regular quadrangular pyramid Sabcd, point O is the center of the base, SB = 20, AC = 24. Find the length of the segment SO.
The diagonals of the square lying at the base are equal and at point O are divided in half, then BD = AC = 24 cm, BO = DO = 24/2 = 12 cm.
Triangle SOB is rectangular, then by the Pythagorean theorem, SO ^ 2 = SB ^ 2 – BO ^ 2 = 400 – 144 = 256.
SO = 16 cm.
Answer: The length of the SO height is 16 cm.
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