What Is the Formula for Finding the Volume of a Trapezoidal Prism?

The formula is the length of the prism times the area of the trapezoid, which is one-half times (a+b) times the height; the area is also called the cross-sectional area. "A" and "B" are the two bases of the trapezoid. The bases are the sides that run parallel to one another, which means they never touch.

The student finds the area of the trapezoid first. If the smaller trapezoid base is 2 and the longer one is 4, she adds those two numbers together to get 6. Then she multiplies that number by the height of the trapezoid, 3, to get 18. Finally, she divides that by 2, which is the same as multiplying by 0.5, to get 9.

To find the volume of the prism, the student multiplies the area of the trapezoid by the length of the prism. If the length of the prism is 10, then she multiplies 9 times 10 to get 90. Therefore, the volume of the trapezoid is 90. The unit depends on the original units the trapezoidal prism was measured in. If it was measured in inches, the resulting unit would be cubic inches, as inches are multiplied by inches three separate times.

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