Use the image to answer the question.
An illustration shows a 3-dimensional vertical rectangular prism that appears as the letter upper C, with a rectangular portion removed from the right center. The rectangular prism is 15 feet high, 10 feet wide, and 1 foot deep. The width of the portion removed from the middle on the right side is 7 feet across. The height of the remaining two arms left at the top and bottom is 4 feet each.
In Los Cabos, Mexico, there is a big sculpture of block letters that welcomes you. The image shows the letter C . What is its surface area?
To find the surface area of the letter C sculpture, we need to calculate the surface area of each individual piece and then subtract the area of the removed rectangle.
1. Calculate the surface area of the front and back pieces of the letter C:
Each front and back piece is a rectangle with dimensions 10ft by 15ft, so the surface area of one front or back piece is:
10ft * 15ft = 150 square feet
Since there are two front and back pieces, the total surface area of the front and back is:
2 * 150 square feet = 300 square feet
2. Calculate the surface area of the top and bottom pieces of the letter C:
Each top and bottom piece is a rectangle with dimensions 10ft by 4ft, so the surface area of one top or bottom piece is:
10ft * 4ft = 40 square feet
Since there are two top and bottom pieces, the total surface area of the top and bottom is:
2 * 40 square feet = 80 square feet
3. Calculate the surface area of the removed rectangle in the middle:
The removed rectangle has dimensions 1ft by 7ft, so the surface area of the removed rectangle is:
1ft * 7ft = 7 square feet
4. Calculate the total surface area of the letter C sculpture:
Total surface area = (300 square feet + 80 square feet) - 7 square feet
Total surface area = 380 square feet
Therefore, the surface area of the letter C sculpture is 380 square feet.