Volume of Trapezoidal Prism
The volume of a trapezoidal prism is the capacity of the prism. It can also be defined as the space inside a trapezoidal prism. A prism has cogruent polygons on top and bottom face and the bases are identical. The side faces of a prism are parallelograms which are known as lateral faces. A prism can be named by the shapes of the two identical faces at its end. A trapezoidal prism is a threedimensional solid that has two trapezoid/trapezium bases at the bottom and top. The shape of the sides faces/ lateral faces of a trapezoidal prism is a parallelogram.
1.  What Is the Volume of Trapezoidal Prism? 
2.  Volume of Trapezoidal Prism Formula 
3.  How To Calculate the Volume of Trapezoidal Prism? 
4.  FAQs on Volume of Trapezoidal Prism 
What Is the Volume of Trapezoidal Prism?
The volume of a trapezoidal prism is the space inside it. A trapezoidal prism is a threedimensional shape with two trapezoidal bases and four parallelogram faces. A prism is a polyhedron with cogruent polygons on top and bottom face and has identical bases. There are two types of trapezoidal prisms oblique and right. In an oblique trapezoidal prism, the side faces are parallelograms and in the right trapezoidal prisms, the side faces are rectangles. In general, a trapezoidal prism means a right trapezoidal prism. Therefore, the side faces are rectangles. So a trapezoidal prism has a total of 6 faces, 12 edges, and 8 vertices. The two bases are in the shape of trapezium or trapezoid that are congruent to each other. It has
 6 faces
 12 edges
 8 vertices
 4 sides: rectangle shape
 Trapezium/Trapezoid as base on bottom and top
Volume of Trapezoidal Prism Formula
The volume of a trapezoidal prism is the capacity of the prism (or) the volume of a trapezoidal prism is the space inside it. It is measured in cubic units such as mm^{3}, cm^{3}, in^{3}, etc. We will see the formulas to calculate the volume trapezoidal prism. The volume of a prism can be obtained by multiplying its base area by total height of the prism. i.e., volume of a prism = base area × height of the prism. We will use this formula to calculate the volume of a trapezoidal prism as well. Consider a trapezoidal prism in which the base has its two parallel sides to be \(b_1\) and \(b_2\), and height to be 'h', and the length of the prism is L. We know that the base of a trapezoidal prism is a trapezium/ trapezoid. Thus,
The area of the base (area of trapezoid) = \(\dfrac{1}{2}{ (b_{1} + b_{2})× h }\)
Now, using the volume of a prism formula (as mentioned above),
The volume of trapezoidal prism = area of base × length = \(\dfrac{1}{2}{ (b_{1} + b_{2})× h } × L\)
How To Calculate the Volume of Trapezoidal Prism?
Following are the steps to calculate the volume of a trapezoidal prism. Make sure that all the measurements are of the same units. Refer to the example that follows.
 Step 1: Identify the parallel sides of the base (trapezoid) to be \(b_1\) and \(b_2\) and the perpendicular distance between them to be \(h\) and find the area of the trapezoid using the formula:
Area of the trapezoid = \(\dfrac{1}{2}{ (b_{1} + b_{2})× h }\)  Step 2: Identify its height / length of the prism (the vertical distance between two bases).
 Step 3: Multiply the base area obtained from step 1 and the height obtained from step 2 to find the volume.
Solved Examples on Volume of Trapezoidal Prism

Example 1: Find the volume of the Trapezoidal Prism with given dimensions.
Solution:
In the above figure, Given that
Base 1 (\(b_1\)) = 6 in, base (\(b_2\)) = 20 in
Height of the trapezoidal base = 12 in
Length of the trapezoid = 17 in
Area of the trapezoid/ trapezium = \(\dfrac{1}{2}{ (b_{1} + b_{2})× h }\)
⇒ A = \(\dfrac{1}{2}\) (6 + 20) × 12
⇒ A = 13 × 12
⇒ A = 156 in^{2}As we know, volume of trapezoidal prism = Area × total length of the trapezoid
⇒ 156^{ }× 17
⇒ 2,652 in^{3 }
Answer: The volume of the Trapezoidal Prism is 2,652 in^{3 }.

Example 2: Calculate the volume of a trapezoidal prism given that the height of the trapezoidal base is 5 cm, and the lengths of its parallel sides are 14 cm and 10 cm, the length of the prism is 6 cm.
Solution:
In the above figure, Given that
Base 1 (\(b_1\)) = 14 cm, base (\(b_2\)) = 10 cm
Height of the trapezoidal base (h) = 5 cm
Total length of the trapezoid = 6 cm
Area of the trapezoid/ trapezium = \(\dfrac{1}{2}{ (b_{1} + b_{2})× h }\)
⇒ A = (1/2) (14 + 10 ) × 5
⇒ A = 12 × 5
⇒ A = 60 cm^{2}As we know, the volume of trapezoidal prism = area × length of the trapezoid
volume = 60^{ }× 6 = 360 cm^{3 }
Answer: The volume of the trapezoidal prism is 360 cm^{3}.
Practice Questions on Volume of Trapezoidal Prism

Question: A trapezoidal prism has a total length of the prism is 4 cm, and the area of its trapezoidal base is 58.5 cm^{2}. Then the volume of the trapezoidal prism is _____.
Answer: 234 cm^{3}.

Question: The volume of the trapezoidal prism in which the base has its parallel sides to be 12 cm and 8 cm, the perpendicular distance between the parallel sides of the base is 10 cm; and the height of the prism is 22 cm is _____.
Answer: 2,200 cm cube.
FAQs on Volume of Trapezoidal Prism
Does a Trapezoidal Prism Have Volume?
A prism is a threedimensional solid. A threedimensional solid has space inside It. The volume is explained as the space inside an object. Thus, a trapezoidal prism has volume as it is a threedimensional shape and is measured in cubic units.
What Do You Mean by the Volume of Trapezoidal Prism?
The volume of a trapezoidal prism is the capacity of the prism. The formula for the volume of a trapezoidal prism is the area of base × height of the prism cubic units.
What Is the Formula To Find the Volume of a Trapezoidal Prism?
The volume of a trapezoidal prism is the product of the area of the base to the height of the prism cubic units. The formula for the volume of the trapezoidal prism is the area of base × height of the prism.
How Can You Calculate the Volume of a Trapezoidal Prism?
The volume of a trapezoidal prism can be calculated by multiplying the area of its trapezoidal faces by its total length.
How Can You Find the Volume of a Trapezoidal Prism when the Height is given?
The height of a prism is the total distance between the two congruent faces of the prism. When the height of a prism is given, the height can be multiplied by the area to find the volume of the trapezoidal prism.
If the Units of Dimensions of a Trapezoidal Prism Are Different, Then How Can You Find the Volume of the Trapezoidal Prism?
If the units of given dimensions of a trapezoidal prism are different then, first we need to change the units of the dimensions of any two dimensions as the unit of the third dimension. After that, we can find the area and the volume of the trapezoidal prism.