what is the total surface area for a rectangular prism if the base is 10.5in, the length 7in, and the height 9.1in
There are six faces to a rectangular prism, so we need to find the area of each face and add them together.
The two bases are each a rectangle with a length of 7in and a width of 10.5in. The area of one base is:
7in x 10.5in = 73.5in²
Since there are two identical bases, we can double this value:
2 x 73.5in² = 147in²
The four other faces are all rectangles with dimensions of 7in x 9.1in, 10.5in x 9.1in, and 10.5in x 7in. The area of each rectangle is:
7in x 9.1in = 63.7in²
10.5in x 9.1in = 95.6in²
Adding up the areas of these four rectangles gives:
(2 x 63.7in²) + (2 x 95.6in²) = 319.6in²
Finally, we add up the areas of all six faces:
147in² + 319.6in² = 466.6in²
Therefore, the total surface area of the rectangular prism is 466.6 square inches.