# SOLUTION: a rectangular prism has height 4 millimeters and width 5 millimeters.If the total surface area is 166 square millimeters, what is the length of the prism

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 Question 117597: a rectangular prism has height 4 millimeters and width 5 millimeters.If the total surface area is 166 square millimeters, what is the length of the prismAnswer by bucky(2189)   (Show Source): You can put this solution on YOUR website!The rectangular prism has two ends that are each 4 mm by 5 mm. The product of 4 mm times 5 mm is 20 sq mm and since there are two of these ends, the total surface area of the ends is 40 sq mm. . This means that the remaining surface area is 166 sq mm minus 40 sq mm = 126 sq mm and this is the surface area that is left for the sides. If L represents the length of the prism, then there are two sides that each have a surface area of 4 mm times L and two sides that each have a surface area of 5 mm times L. That means that the remaining surface area can be calculated from: . 2(4L + 5L) = 2(9L) = 18L . So: . 18L = 126 sq mm . Solve for L by dividing both sides by 18 and you get: . L = 126/18 = 7 mm . Hope this shows you a way through the problem. It probably would be a little more understandable if you made a sketch. .