The two edges of a rectangular parallelepiped extending from one vertex are 12

The two edges of a rectangular parallelepiped extending from one vertex are 12 and 5, and the volume of the parallelepiped is 540. Find the surface area of this parallelepiped.

Since the volume is equal to the product of the area and the height, the height is: 12 * 5 * x = 540, where x = 9.

To find the total surface area, you need to find the base area and side area.

The lateral surface area is: (12 + 5) * 2 * 9 = 306.

And the area of the base is: 12 * 5 = 60.

Then the total surface area is: 306 + 2 * 60 = 426.