In a regular quadrilateral pyramid SABCD, point O is the center of the base, S is the vertex, CS = 17, BD = 16.

| February 19, 2021 | education

In a regular quadrilateral pyramid SABCD, point O is the center of the base, S is the vertex, CS = 17, BD = 16. Find the length of the segment SO.

Because we know that the pyramid is regular and quadrangular, so its base is the square ABCD. By the hypothesis of the problem, we know the diagonal; it is BD. All diagonals of the square are equal, so BD = AC. Let’s find what is half of the OS diagonal.

1) 16/2 = 8.

In a regular pyramid, the height falls to the center of the base, i.e. SO and OS are perpendicular to each other, and triangle SOC is rectangular with legs SO and OS. The diagonal is known, it is equal to 17, we found the leg of the OS, we find the value SO:

2) √17 ^ 2 – 8 ^ 2 = √289 – 64 = √225 = 15.

Answer: The height of the pyramid is 15.



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