what is the missing length of rectangular prism if height and width are both 8 inches and surface area is 156 in 2 step by step
To find the missing length of the rectangular prism, we first need to calculate the total surface area of the prism and then use that information to determine the missing length.
1. Calculate the total surface area:
The surface area of a rectangular prism is given by the formula:
Surface Area = 2(length x width) + 2(length x height) + 2(width x height)
Given that the height and width are both 8 inches, we can substitute these values into the formula:
156 = 2(length x 8) + 2(length x 8) + 2(8 x 8)
156 = 16length + 16length + 128
156 = 32length + 128
156 - 128 = 32length
28 = 32length
length = 28 / 32
length = 0.875 inches
Therefore, the missing length of the rectangular prism is 0.875 inches.