In the regular quadrangular pyramid SABCD, point O is the center of the base, s is the vertex, SO = 12

In the regular quadrangular pyramid SABCD, point O is the center of the base, s is the vertex, SO = 12, AC = 18. Find the side rib SB

Consider the triangle AOS: the angle O is 90 ° (the height SO is perpendicular to the base ABCD), SO = 12, AO = 1/2 * AC = 1/2 * 18 = 9 (since the diagonals of the square ABCD intersect in the middle).

By the Pythagorean theorem:

AS² = SO² + AO² = 12² + 9² = 144 + 81 = 225.

AS = √225 = 15.

Since the ABCD pyramid is correct, all side edges are equal, which means SB = SA = 15.

Answer: the side edge SB is 15.