A cube and a rectangular parallelepiped have equal volumes, find the area of the cube if the length

A cube and a rectangular parallelepiped have equal volumes, find the area of the cube if the length of the rectangular parallelepiped is 12 cm, which is 2 times the width and 4 times the height of the parallelepiped.

Let’s write down the measurements of a rectangular parallelepiped:
a1 = 12 cm;
b1 = a1 / 2 = 12/2 = 6 cm;
c1 = a1 / 4 = 12/4 = 3 cm.

Let’s calculate the volume of this parallelepiped:
V = a1 * b1 * c1 = 12 * 6 * 3 = 216 cm³.

By condition, the cube has the same volume: 216 cm³. Let’s calculate what the edge of the cube is equal to:
V = a³;
a³ = 216;
a = 6 cm.

Let’s calculate the base area of the cube:
S main = a² = 6² = 36 cm².

Let’s define the surface area of the cube:
S pov = 6 * a² = 6 * 6² = 216 cm².

Answer: the base area of this cube is 36 cm², and its surface area is 216 cm².