The construction of a rectangular prism depends on three measurements: its height, length and width. Prisms are threedimensional objects that have two identical polygon shapes at the ends, also called the bases. The length and width measurements of a prism determine the dimensions of its bases, while the height measurement determines the distance between the bases. A rectangular prism's height can be calculated from its volume, which equals base area times height, or its surface area, which equals two times the base area plus base perimeter times height.
From Volume

Obtain the volume of the prism. In this example, let the volume be 3,000.

Multiply the base's length and width together to calculate the base area. In this example, the base has a width measurement of 10 and a length measurement of 15, and 10 multiplied by 15 equals 150.

Divide the base area into the prism's volume to calculate the height measurement. Concluding this example, dividing 3,000 by 150 equals 20. The height is 20.
From Surface Area

Obtain the surface area of the prism. In this example, allow the surface area to be 2,700.

Calculate the base area of the prism by multiplying the measurements for length and width and then doubling the area. In this example, the width is 15 and the length is 20. Multiplying 15 by 20 results in 300, and multiplying 300 by 2 equals 600.

Subtract the doubled base area from the surface area. In this example, subtracting 600 from 2,700 equals 2,100.

Calculate the perimeter of the base area by doubling the length, then doubling the width and then adding the two products together. In this example, 15 multiplied by 2 is 30, 20 multiplied by 2 is 40, and 30 added to 40 is 70.

Divide the base perimeter into the difference from Step 3 to calculate the height of the prism. Concluding this example, dividing 2,100 by 70 results in 30. The height of the prism is 30.
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