The edge of the cube is 4 cm. Find the cross-sectional area passing through the diagonals of two adjacent cube boundaries.

The section passing through the diagonals of two adjacent faces of the cube also passes through the diagonal of the third face, which is perpendicular to the first two. Such a section is an equilateral triangle, since all the faces in the cube are equal, which means that their diagonals are also equal.
The diagonal of a cube face can be found as the hypotenuse of a right-angled triangle, in which the legs are the edges of the cube.
The sum of the squares of the legs is equal to the square of the hypotenuse, we find the diagonal: d = √ (4 ^ 2 + 4 ^ 2) = √16 * 2 = 4√2 cm.
The area of ​​an equilateral triangle can be determined by the formula: S = (√3 * a ^ 2) / 4, where a is the side of the triangle.
S = (√3 * (4√2) ^ 2) / 4 = √3 * 16 * 2/4 = 8√3≈13.86 cm2.