Through the point O of the intersection of the diagonals of the square, the side of which is 8 cm, a straight line OK is drawn

Through the point O of the intersection of the diagonals of the square, the side of which is 8 cm, a straight line OK is drawn, perpendicular to the plane of the square. Find the distance from point K to the top of the square if OK = 10cm.

According to the condition of the problem, we got a regular quadrangular pyramid KABCD.
By the Pythagorean theorem, we find the diagonal of the square lying at the base of the pyramid:
AC = √ (AB² + BC²) = √ (64 + 64) = √128 = 8√2 (cm).
Half of the diagonal is equal to:
AO = 1/2 * AC = 4√2 (cm).
In the right-angled triangle AOK, we find the hypotenuse of the KA – this is the distance from point K to the top of the square:
KA = √ (OK² + AO²) = √ (100 + 32) = √132 = 2√33 (cm).
Answer: KA = 2√33 cm.