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Answer :
Final answer:
The total surface area of the square prism (box) is 176 square inches, calculated by adding the area of the two square bases and the lateral faces together.
Explanation:
To find the total surface area of the square prism (which is also known as a box), we need to calculate the area of all of its faces. Since the base of the box is a square with an area of 16 square inches, each side of the square base is 4 inches (since 4 inches x 4 inches = 16 square inches). The box has two bases (top and bottom) and four lateral faces. The height of the box is 9 inches.
- Calculate the area of the two bases: 16 square inches (base area) x 2 (top and bottom) = 32 square inches.
- Calculate the area of one of the lateral faces: 9 inches (height) x 4 inches (side of the base) = 36 square inches. Since there are four lateral faces, multiply by 4 to get the total lateral surface area: 36 square inches x 4 faces = 144 square inches.
- Finally, add the area of the bases to the lateral surface area to find the total surface area: 32 square inches (bases) + 144 square inches (lateral faces) = 176 square inches.
Therefore, the total surface area of the box is 176 square inches.
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