The base of the prism is a regular hexagon. Its side faces are squares. The largest diagonal

The base of the prism is a regular hexagon. Its side faces are squares. The largest diagonal of the prism is 10 cm. Find the side of the base.

Let the length of the edge of a regular hexagon be X cm.

Since the side faces of the prism are squares, the height of the prism is also X cm.

Let’s construct large diagonals at the base of the prism. Diagonals divide a regular hexagon into six equilateral equal triangles with side X cm.

Then the diagonal AD = OA + OD = X + X = 2 * X.

In a right-angled triangle ADD1, according to the Pythagorean theorem, AD1 ^ 2 = AD ^ 2 + DD1 ^ 2.

100 = 4 * X ^ 2 + X ^ 2 = 5 * X ^ 2.

X ^ 2 = 100/5 = 20.

X = 2 * √5 cm.

Answer: The side of the base is 2 * √5 cm.