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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