An illustration shows a 3 D box with length of 27 centimeters labeled as front, a width of 20 centimeters, and height of 20 centimeters.
A box needs to be decorated to use as a prop in a play. The bottom and the back of the box do not need to be decorated. What is the surface area of the box that needs to be decorated?
To find the surface area of the box that needs to be decorated, we need to calculate the areas of the top, front, and sides of the box.
The top of the box has a length and width of 27 cm and 20 cm respectively. Therefore, the area of the top is 27 cm * 20 cm = 540 square cm.
The front of the box has a length and height of 27 cm and 20 cm respectively. So, the area of the front is 27 cm * 20 cm = 540 square cm.
The sides of the box have widths of 20 cm and heights of 20 cm. Since the box is rectangular, there are 2 sides. Thus, the area of the sides is 2 * (20 cm * 20 cm) = 800 square cm.
Adding up the areas of the top, front, and sides, we get the total surface area of the box that needs to be decorated:
540 square cm (top) + 540 square cm (front) + 800 square cm (sides) = 1880 square cm.
Therefore, the surface area of the box that needs to be decorated is 1880 square cm.