How this calculator works
The volume of any prism is the area of its uniform cross section multiplied by its length. Here the cross section is a trapezoid, whose area is the average of the two parallel sides multiplied by the perpendicular height between them. Multiply that end area by the prism length and the volume follows. This calculator assumes the trapezoid is isosceles, which is the usual case and lets the sloping side be found from the height and half the difference of the parallel sides.
Formula
End area = (a + b)/2 × h; volume = end area × length; sloping side = √(h² + ((a - b)/2)²); perimeter = a + b + 2 × sloping side.
Worked example
A prism with parallel sides of 4 m and 2 m, a trapezoid height of 3 m and a length of 10 m has an end area of (4 + 2)/2 × 3 = 9 m² and a volume of 9 × 10 = 90 m³. Its sloping sides are √10 ≈ 3.162 m each.
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Frequently asked questions
Is the trapezoid height the same as the prism length?
No. The trapezoid height is measured inside one end face between the parallel sides. The prism length is the separate distance between the two end faces, at right angles to them.
What if the trapezoid is not isosceles?
The volume is unchanged, because it depends only on the end area and length. The sloping side lengths and perimeter would differ, so the perimeter and leg outputs would need the individual side lengths.
Can one parallel side be zero?
Yes. A trapezoid with a top side of zero becomes a triangle, and the formula still gives the right volume. Both parallel sides cannot be zero at once, since the end face would have no area.