# Volume of a Trapezoidal Prism

The volume of a trapezoidal prism is the space it occupies in the three-dimensional plane. It is measured in cubic units such as m3, cm3, mm3, ft3.

## Formula

The formula is given below:

Let us solve some examples to understand the concept better.

## Solved Examples

Find the volume of a trapezoidal prism given in the figure.

Solution:

As we know,
${Volume\left( V\right) =\dfrac{1}{2}\left( a+b\right) \times h\times l}$, here a = 10 cm, b = 8 cm, h = 6 cm, l = 13 cm
${\therefore V=\dfrac{1}{2}\times \left( 10+8\right) \times 6\times 13}$
= 702 cm3

Finding the volume of a trapezoidal prism when BASE AREA and LENGTH are known

Find the volume of a trapezoidal prism given in the figure, whose base area is 361 m2 and length is 12.5 m.

Solution:

Here we will use an alternative formula.
Volume (V) = Base Area Ã— l, here base area = 361 m2, l = 12.5 m
âˆ´V = 361 Ã— 12.5
= 4512.5 m3

Finding the volume of an oblique trapezoidal prism when BASE AREA and LENGTH are known

Find the volume of an oblique trapezoidal prism given in the figure.

Solution:

As we know,
Volume of a right trapezoidal prism with length ‘l’ = Volume of oblique trapezoidal prism length ‘l’
${Volume\left( V\right) =\dfrac{1}{2}\left( a+b\right) \times h\times l}$, here a = 12 m, b = 9 m, h = 5 m, l = 11 m
${\therefore V=\dfrac{1}{2}\times \left( 12+9\right) \times 5\times 11}$
= 577.5 m3

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