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To find the length of the diagonal of the prism, we need to use the Pythagorean theorem.
Let's consider the right triangle formed by the diagonal, the height, and the length of the prism.
Using the Pythagorean theorem, we have:
(diagonal)^2 = (height)^2 + (length)^2
(diagonal)^2 = (12 cm)^2 + (4 cm)^2
(diagonal)^2 = 144 cm^2 + 16 cm^2
(diagonal)^2 = 160 cm^2
Taking the square root of both sides, we get:
diagonal = √160 = √(16 x 10) = 4√10 cm
Therefore, the length of the diagonal of the prism is 4√10 centimeters.