Correct Answer
Option C (56) should be selected.
Explanation
There are several approaches to determine the surface area of this three-dimensional solid figure. One approach is to determine the surface area of the front face and know that the surface area of the back face will be the same. Then we would add the surface area of the faces around the side of the figure.
The front face is made up of three squares that are each 2 feet by 2 feet. Each little square has an area of 4 square feet, and since there are three of them, the area of the front face is 3 times 4 equals 12 \( 3 \times 4 = 12 \) square feet. We multiply this by 2 to get the combined surface area of the front and back faces: 12 times 2 equals 24 \( 12 \times 2 = 24 \) square feet.
Then, there are six faces around the figure, one on the bottom that is 4 feet by 2 feet, another on the right side that is also 4 feet by 2 feet. Each of these has an area of 8 square feet. Then, we have one on the top, one on the left, one cutting into the middle from the left, and one cutting into the middle from the top. Each of these has an area of 2 feet times 2 feet, or 4 square feet. Adding the areas of all the faces, we get a total surface area for the figure of24 plus open parenthesis 2 close parenthesis open parenthesis 8 close parenthesis, plus open parenthesis 4 close parenthesis open parenthesis 4 close parenthesis, which equals 24 plus 16 plus 16, which equals 56 square feet.
$$ 24 + (2)(8) + (4)(4) = 24 + 16 + 16 = 56 \text{ square feet} $$