A box is in the shape of a square prism. The height of the box is 8 inches, and the area of the square base is 16 square inches. What is the total surface area in square inches of the box?
The total surface area of the box is 160 square inches.
To find the total surface area of the box, we need to consider the area of all the faces.
- The area of the square base (since all sides of a square are equal) = 16 square inches.
- The area of the other square face (the top face) is the same as the base, so it's also 16 square inches.
- There are four sides of the box (all rectangles) with dimensions: length = 8 inches (height of the box) and width = 4 inches (half the length of one side of the square base), so each of these side faces has an area of 32 square inches.
So, the total surface area of the box is:
2 × (16 square inches) + 4 × (32 square inches)
= 32 square inches + 128 square inches
= 160 square inches
So, the total surface area of the box is 160 square inches.
Surface Area of a Square Prism
The surface area of a square prism is the sum of the areas of all its faces. To calculate it, we need some information:
- Side length of the square base (s): This is the length of one side of the square at the base of the prism.
- Height of the prism (h): This is the distance from any point on the base to the corresponding point on the opposite face.
Once you have these values, you can use the following formula to find the surface area:
Surface Area = 2 * Base Area + Lateral Surface Area
Base Area = s^2 (area of one square base)
Lateral Surface Area = Perimeter of base * Height
Perimeter of base = 4 * s (since all sides of a square are equal)
Putting everything together:
Surface Area = 2 * s^2 + 4 * s * h
Alternatively, you can express it as: Surface Area = 2(s^2 + 2sh)
Example:
If the side length of the square base is 5 cm and the height of the prism is 3 cm, then:
Surface Area = 2 * 5^2 + 4 * 5 * 3 = 50 + 60 = 110 cm^2
Remember to include the units (e.g., cm^2, in^2) in your final answer.
