The surface area of the prism is 108 square centimeters.
The surface area of a prism is the sum of the areas of all of its faces. In the case of a rectangular prism, there are six faces: two bases, two long sides, and two short sides.
To find the surface area of the prism in the image, we need to find the areas of each of these faces and add them all together.
Base:
The area of a rectangle is equal to the length times the width. From the image, we can see that the length of the base is 6 cm and the width is 3 cm. Therefore, the area of each base is:
Area of base = 6 cm * 3 cm = 18 cm²
Long sides:
The long sides of the prism are rectangles as well. From the image, we can see that the length of a long side is 9 cm and the width is 3 cm. Therefore, the area of each long side is:
Area of long side = 9 cm * 3 cm = 27 cm²
Short sides:
The short sides of the prism are squares. From the image, we can see that the side length of each square is 3 cm. Therefore, the area of each short side is:
Area of short side = 3 cm * 3 cm = 9 cm²
Total surface area:
Now that we have found the areas of each of the faces, we can add them all together to find the total surface area of the prism:
Total surface area = 2 * area of base + 2 * area of long side + 2 * area of short side
Total surface area = 2 * 18 cm² + 2 * 27 cm² + 2 * 9 cm²
Total surface area = 36 cm² + 54 cm² + 18 cm²
Total surface area = 108 cm²
Therefore, the surface area of the prism is 108 square centimeters.