For a rectangular box, what is the product of the areas of the 3 adjacent faces that meet at a point?

For a rectangular box, let's denote the dimensions of the box as a, b, and c. The three adjacent faces that meet at a corner can be represented by the pairs of dimensions as follows: 1. Face with dimensions a and b has an area of A1 = ab 2. Face with dimensions b and c has an area of A2 = bc 3. Face with dimensions c and a has an area of A3 = ca To find the product of the areas of these three faces, we calculate: A1×A2×A3 = (ab)(bc)(ca) Now, we simplify this expression: A1×A2×A3= ab×bc×ca = a² × b² ×c² = (abc)² Thus, the product of the areas of the three adjacent faces that meet at a point is: (abc)²