Find the side edge of a regular four-sided pyramid if its volume is 4cm3 and the other side of the base is 2cm.

Let’s use the formula for the volume of a pyramid.

V = S * h / 3.

By condition, V = 4 cm3, the side at the base is 2 cm. Then S = 2 * 2 = 4 cm2.

4 = 4 * h / 3.

h = FO = 3 cm.

By the Pythagorean theorem, we find the diagonal of the base of the pyramid AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 4 + 4 = 8.

AC = √8 = 2 * √2.

Then, AO = AC / 2 = √2.

Consider a right-angled triangle AOF, and by the Pythagorean theorem we find AF.

AF ^ 2 = AO ^ 2 + OF ^ 2 = 2 + 9 = 11.

AF = √11.

Answer: The side edge is equal to √11.



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