How To Find Volume Trapezoidal Prism

Volume of Trapezoidal Prism

The volume of a trapezoidal prism is the chapters of the prism. It can besides exist divers every bit 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 stop. A trapezoidal prism is a iii-dimensional solid that has two trapezoid/trapezium bases at the bottom and meridian. The shape of the sides faces/ lateral faces of a trapezoidal prism is a parallelogram.

What Is the Book of Trapezoidal Prism?

The book of a trapezoidal prism is the space inside information technology. A trapezoidal prism is a three-dimensional shape with two trapezoidal bases and 4 parallelogram faces. A prism is a polyhedron with cogruent polygons on superlative and bottom face up and has identical bases. There are 2 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. And so a trapezoidal prism has a total of half dozen faces, 12 edges, and viii vertices. The two bases are in the shape of trapezium or trapezoid that are coinciding to each other. It has

• 6 faces
• 12 edges
• 8 vertices
• iv sides: rectangle shape
• Trapezium/Trapezoid every bit base on lesser 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 equally mm³, cm^three, in³, etc. We will see the formulas to calculate the book trapezoidal prism. The volume of a prism tin be obtained by multiplying its base area by total meridian of the prism. i.e., volume of a prism = base area × height of the prism. We volition use this formula to calculate the volume of a trapezoidal prism equally well. Consider a trapezoidal prism in which the base of operations has its two parallel sides to exist \(b_1\) and \(b_2\), and meridian to exist '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 of operations (area of trapezoid) = \(\dfrac{1}{2}{ (b_{i} + b_{ii})× h }\)

Now, using the volume of a prism formula (equally mentioned higher up),

The volume of trapezoidal prism = area of base × length = \(\dfrac{1}{2}{ (b_{one} + b_{2})× h } × L\)

How To Summate 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 case that follows.

• Step 1: Identify the parallel sides of the base of operations (trapezoid) to be \(b_1\) and \(b_2\) and the perpendicular altitude between them to be \(h\) and notice the area of the trapezoid using the formula:
  Surface area of the trapezoid = \(\dfrac{1}{2}{ (b_{1} + b_{2})× h }\)
• Step 2: Place its height / length of the prism (the vertical distance betwixt two bases).
• Pace 3: Multiply the base area obtained from step 1 and the height obtained from step 2 to observe the book.

Examples on Volume of Trapezoidal Prism​​​​​

1. Example ane: Find the book of the Trapezoidal Prism with given dimensions.

   

   Solution:

   In the above effigy, Given that

   Base one (\(b_1\)) = 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 = \(\dfrac{ane}{2}{ (b_{ane} + b_{2})× h }\)

   ⇒ A = \(\dfrac{1}{ii}\) (6 + 20) × 12
   ⇒ A = 13 × 12
   ⇒ A = 156 in^two

   As we know, volume of trapezoidal prism = Area × full length of the trapezoid

   ⇒ 156 × 17

   ⇒ 2,652 in³

   Respond: The volume of the Trapezoidal Prism is 2,652 in^three .

2. 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 fourteen cm and ten cm, the length of the prism is half-dozen cm.

   Solution:

   In the above effigy, Given that

   Base 1 (\(b_1\)) = 14 cm, base (\(b_2\)) = x cm

   Height of the trapezoidal base (h) = five cm

   Full length of the trapezoid = 6 cm

   Area of the trapezoid/ trapezium = \(\dfrac{1}{2}{ (b_{1} + b_{2})× h }\)

   ⇒ A = (1/2) (fourteen + 10 ) × 5
   ⇒ A = 12 × five
   ⇒ A = 60 cm^two

   As we know, the book of trapezoidal prism = surface area × length of the trapezoid

   volume = lx × 6 = 360 cm³

   Answer: The book of the trapezoidal prism is 360 cm³.

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Practice Questions on Book of Trapezoidal Prism

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FAQs on Volume of Trapezoidal Prism

Does a Trapezoidal Prism Have Book?

A prism is a three-dimensional solid. A three-dimensional solid has space within Information technology. The volume is explained equally the space within an object. Thus, a trapezoidal prism has volume as it is a three-dimensional shape and is measured in cubic units.

What Do You Hateful by the Volume of Trapezoidal Prism?

The volume of a trapezoidal prism is the capacity of the prism. The formula for the book of a trapezoidal prism is the area of base × meridian of the prism cubic units.

What Is the Formula To Discover the Volume of a Trapezoidal Prism?

The volume of a trapezoidal prism is the product of the area of the base to the superlative of the prism cubic units. The formula for the volume of the trapezoidal prism is the area of base × pinnacle of the prism.

How Can Y'all Calculate the Volume of a Trapezoidal Prism?

The volume of a trapezoidal prism can exist calculated by multiplying the area of its trapezoidal faces past its full length.

How Can You lot Find the Volume of a Trapezoidal Prism when the Height is given?

The height of a prism is the total distance between the 2 congruent faces of the prism. When the meridian of a prism is given, the acme tin can be multiplied by the expanse 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 whatsoever 2 dimensions as the unit of the 3rd dimension. After that, we tin find the surface area and the volume of the trapezoidal prism.

Source: https://www.cuemath.com/measurement/volume-of-trapezoidal-prism/

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