The height RO of the pyramid is perpendicular to the base plane, then the triangle AOP is rectangular, from which we determine the length of the leg OA by the Pythagorean theorem.
OA ^ 2 = PA ^ 2 – PO ^ 2 = 16 – 9 = 7.
ОА = √7 cm.
At the base of the pyramid is a square, the diagonals of which, at the point of intersection, are divided in half, then AC = 2 * OA = 2 * √7 cm.
Answer: The diagonal of the base of the pyramid is 2 * √7 cm.
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