Surface Area Unit Test

Question

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Question
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?

(1 point)
ft.2

Answer 1

To find the surface area of the letter C sculpture, we need to calculate the surface area of each individual rectangular prism section and then add them together.

1. The front side of the C is a rectangle with dimensions 15 feet by 10 feet, so the surface area is:
15 ft * 10 ft = 150 ft^2

2. The top arm of the C is a rectangle with dimensions 15 feet by 4 feet, so the surface area is:
15 ft * 4 ft = 60 ft^2

3. The bottom arm of the C is also a rectangle with dimensions 15 feet by 4 feet, so the surface area is also:
15 ft * 4 ft = 60 ft^2

4. The side arm of the C is a rectangle with dimensions 4 feet by 1 foot, but we need to subtract the rectangle removed from the middle, which is 7 feet by 1 foot, so the surface area is:
(4 ft * 1 ft) - (7 ft * 1 ft) = (4 ft - 7 ft) * 1 ft = -3 ft^2

(Note: The negative sign indicates that this area should be subtracted)

Now, let's add the surface areas together:
150 ft^2 + 60 ft^2 + 60 ft^2 - 3 ft^2 = 267 ft^2

Therefore, the surface area of the letter C sculpture is 267 ft^2.