Answer:
surface area of the rectangular prism is 278( 1/4) cm^2,
Explanation:
To calculate the surface area of a rectangular prism, we need to find the area of all six faces and add them together.
The formula for the surface area of a rectangular prism is:
Surface area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism.
Given that the dimensions of the rectangular prism are 5 and three-fourths cm by 4 cm by 11 and three-fourths cm, we can substitute these values in the formula to get:
Surface area = 2(5 3/4 x 4) + 2(5 3/4 x 11 3/4) + 2(4 x 11 3/4)
Simplifying this expression, we get:
Surface area = 2(23) + 2(69 1/8) + 2(47)
Surface area = 46 + 138 1/4 + 94
Surface area = 278 1/4 cm^2
Therefore, the surface area of the rectangular prism is 278 1/4 cm^2, which is closest to the option: two hundred seventy-five and one-eighth cm^2.