Find the side edge of a regular quadrangular pyramid if the side of the base is 6 and the height is 3√14.
| July 25, 2021 | education
Since the pyramid is correct, ABCD is a square.
Determine the length of the diagonal AC of the base of the pyramid.
AC ^ 2 = AB ^ 2 + BC ^ 2 = 36 + 36 = 72.
AC = 6 * √2 cm.
The diagonals of the square ABCD, at the point of their intersection, are divided in half, then AO = AC / 2 = 6 * √2 / 2 = 3 * √2 cm.
In a right-angled triangle AOE, according to the Pythagorean theorem, AE ^ 2 = AO ^ 2 + OE ^ 2 = 18 + 126 = 144.
AE = 12 cm.
Answer: The length of the side edge of the pyramid is 12 cm.
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