In a regular quadrangular pyramid S ABCD, point O is the center of the base, S is the apex, SO = 3 AC = 8.
| July 2, 2021 | education
In a regular quadrangular pyramid S ABCD, point O is the center of the base, S is the apex, SO = 3 AC = 8. Find the SD side rib.
At the base of a regular pyramid is a square.
The diagonals of the square lying at the base of the pyramid, at the point of their intersection, are divided in half, then CO = AO = AC / 2 = / 2 = 4 cm.
In a right-angled triangle SОС, we define the length of the hypotenuse SС.
SC ^ 2 = SO ^ 2 + OC ^ 2 = 9 + 16 = 25.
SC = √25 = 5 cm.
The side edges of the regular pyramid are equal, then SD = SC = 5 cm.
Answer: The length of the side rib SD = 5 cm.
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