Prisms are geometric solids that come in many different shapes and an infinite number of sizes. Prism are often distinguished by the shape of their base polygon. A prism having trapezoid base faces is called a trapezoidal prism.

Where, a, b be length of the top and bottom of the trapezoid and h be the height of the trapezoidal. And 'l' be the length or height of the trapezoidal prism.

Volume of a Trapezoidal Prism

The volume of a right trapezoidal prism is equal to the height times the base area of the trapezoid. The area of trapezoid is $\frac{1}{2}$h(a + b) and 'h' is the height of the trapezoid, not the height of the prism. If 'a' is the length of the top, 'b' is the length of the bottom. Then the formula for the volume of the trapezoidal prism is given below:

Volume of a Trapezoidal Prism Formula

The volume of a prism is given by the formula,

V = Al

Where A is the area of the base of the prism and 'l' is the length or height of the prism.

=> Area of trapezoidal prism = $\frac{1}{2}$h(a + b)

=> Volume of the Trapezoidal Prism = $\frac{1}{2}$h(a + b) x l

= $\frac{1}{2}$h(a + b)l

Formula:

Volume of the Trapezoidal Prism =
$\frac{1}{2}$h(a + b)l

Where, a = Length of the top, b = Length of the bottom, h = Height of the trapezoidal and l = Height of the prism.

Octagonal Prism

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