The point is removed from each side of the square by 10 cm, located at a distance of 8 cm

The point is removed from each side of the square by 10 cm, located at a distance of 8 cm from the plane of the square. Find the plane of the square

Let us denote the square given by the condition ABCD, the point that is 10 cm away from the sides – point K. We get a pyramid.
The distance from point K to the side of the square – apothem, we denote KM.
The distance from point K to the plane of the square is the height of the pyramid – KН.
Consider a right-angled triangle KНM, find, by the Pythagorean theorem, the leg НM – half of the side of the square ABCD. |
HM = √ (KM² – KH²) = √ (100 – 64) = √36 = 6 (cm).
The side of the square is 2 * 6 = 12 (cm).
S ABCD = 12² = 144 (cm²).
Answer: the area of the square is 144 cm².