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 three-dimensional 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 three-dimensional 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 mm3, cm3, in3, 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.
Examples on Volume of Trapezoidal Prism
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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 in2As we know, volume of trapezoidal prism = Area × total length of the trapezoid
⇒ 156 × 17
⇒ 2,652 in3
Answer: The volume of the Trapezoidal Prism is 2,652 in3 .
FAQs on Volume of Trapezoidal Prism
Does a Trapezoidal Prism Have Volume?
A prism is a three-dimensional solid. A three-dimensional 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 three-dimensional 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.