In the regular quadrangular pyramid SABCD, the point is O-center of the base, S-vertex
| May 3, 2021 | education
In the regular quadrangular pyramid SABCD, the point is O-center of the base, S-vertex, SO = 16. BD = 24. Find the side rib SA.
The base of a regular quadrangular pyramid is a square, then its diagonals AC and BD are equal in length.
AC = BD = 24 cm.
Point O divides the diagonals of the square in half, then the length of the segment OA = AC / 2 = 24/2 = 12 cm.
In a right-angled triangle SOA, by the Pythagorean theorem, we determine the length of the hypotenuse SA.
SA ^ 2 = SO ^ 2 + OA ^ 2 = 16 ^ 2 + 12 ^ 2 = 256 + 144 = 400.
SA = 20cm.
Answer: The lateral edge SA is 20 cm.
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