Final answer:
The lateral area of the cube is 216cm² and the total area is 288cm².
Step-by-step explanation:
To find the lateral area of a cube, we need to find the area of all the lateral faces. A cube has 6 faces, all of which are squares. So, the lateral area of a cube is 6 times the area of one of its faces.
The area of a square is found by multiplying the length of one side by itself. Since the edge length of the cube is 6cm, the lateral area of the cube is 6 times (6cm * 6cm) = 216cm².
The total area of a cube is found by adding the lateral area and the area of the two bases. The area of each base is found by multiplying the length of one side by itself. So, the total area of the cube is 6 times (6cm * 6cm) + 2 times (6cm * 6cm) = 216cm² + 72cm² = 288cm².