To find the surface area that needs to be decorated, we need to find the areas of the front, top, and sides of the box.
Front:
Area of front = length * height
Area of front = 27 cm * 20 cm
Area of front = 540 cm²
Top:
Area of top = length * width
Area of top = 27 cm * 20 cm
Area of top = 540 cm²
Sides:
There are two sides that need to be decorated, the left side and the right side.
Area of each side = height * width
Area of each side = 20 cm * 20 cm
Area of each side = 400 cm²
Total surface area that needs to be decorated = Area of front + Area of top + 2(Area of side)
Total surface area that needs to be decorated = 540 cm² + 540 cm² + 2(400 cm²)
Total surface area that needs to be decorated = 540 cm² + 540 cm² + 800 cm²
Total surface area that needs to be decorated = 1880 cm²
Therefore, the surface area of the box that needs to be decorated is 1880 cm².