In a regular quadrangular pyramid SABCD, point O is the center of the base, S is the apex, SO = 12

In a regular quadrangular pyramid SABCD, point O is the center of the base, S is the apex, SO = 12, S = 13. Find the length of the speaker.

Let’s construct the diagonals AC and BD at the base of the pyramid.

The height SO is perpendicular to the plane of the base, then the triangle SOD is rectangular, in which, using the Pythagorean theorem, we define the segment OD.

OD ^ 2 = SD ^ 2 – SO ^ 2 = 169 – 144 = 25.

OD = 5 cm.

In a regular quadrangular pyramid, the base is a square ABCD, in which point O divides the diagonals BD and AC in half, then BD = 2 * OD = 2 * 5 = 10 cm.

Since AC = BD, AC = 10 cm.

Answer: The length of the AC diagonal is 10 cm.