Trapezoidal Prism
A trapezoidal prism is a 3D figure made up of two trapezoids that is joined by four rectangles. Prisms consist of polygons that form their bases. One of the most recognizable examples of a trapezoid prism is a brick especially the circular fire pit brick. A trapezoidal prism comes from the shape trapezoid. Let's learn more about its definition, properties, formulas and solve a few examples.
| 1. | Trapezoidal Prism Definition |
| 2. | Trapezoidal Prism Properties |
| 3. | Trapezoidal Prism Net |
| 4. | Volume of a Trapezoidal Prism |
| 5. | Surface Area of a Trapezoidal Prism |
| 6. | FAQs on Trapezoidal Prism |
Trapezoidal Prism Definition
A trapezoidal prism is a 3D figure which has trapezoid cross-sections in one direction and rectangular cross-sections in the other direction which means the prism has two congruent trapezoids that are connected to each other with four rectangles. These congruent trapezoids are on the top and bottom of the prism which are called bases. The four rectangles are called the lateral faces of the trapezoid prism. A trapezoidal prism has six faces, eight vertices, and 12 edges. To construct a trapezoidal prism, we need to draw a trapezoid first that has two parallel sides and a height i.e. distance between the sides. The image below describes how a trapezoid prism looks like. H indicates the height of the trapezoid, S indicates the surface area, L indicates the lateral area, and B1 and B2 indicate the lengths of the base.
Trapezoidal Prism Properties
The properties of a trapezoid prism are very similar to that of a trapezoid, they are listed below:
- A trapezoid prism consists of two trapezoids that are joined by four rectangles
- A trapezoid prism consists of eight vertices
- A trapezoid prism consists of six faces
- A trapezoid prism consists of 12 edges
- A trapezoid prism is a polygon that consists of trapezoids
Trapezoidal Prism Net
The net of the trapezoidal prism consists of six faces, eight vertices, and 12 edges. When the trapezoidal prism is opened flat, we can see the four rectangle-shaped objects that help in joining the two trapezoid-shaped objects together to form a trapezoidal prism. The image below demonstrates the flattened version of a trapezoidal prism.
Volume of a Trapezoidal Prism
To find the volume of a trapezoidal prism, we need to multiply the area of the base by the height. The area is calculated as the surface area of one of the trapezoids by the distance between the two trapezoids. Therefore, in order to find the volume of a trapezoidal prism, we need to first find the area of one trapezoid. Hence, to find the volume of a trapezoidal prism we can use these formulas:
Volume of a Trapezoidal Prism = A × I cubic units
Area (A) = ½ × h × (a + b) or ½ h(b1+ b2)
Where h is the height of the trapezoid, l is the height of the prism, a and b are the lengths of the top and bottom of a trapezoidal prism
Surface Area of a Trapezoidal Prism
The surface area of a trapezoidal prism is calculated by multiplying the surface area of one of the prisms by two then adding the sum of the perimeter into the height of the trapezoidal prism. The formula for calculating the trapezoidal prism is:
Surface Area of a Trapezoidal Prism = h (b + d) + l (a + b + c + d) square units
where h is the height, b and d are the lengths of the base, a + b + c + d is the perimeter, and l is the lateral surface area. To understand this better, you can check out the page on how to find the surface area of a trapezoidal prism.
Related Topics
Listed below are a few interesting topics related to the trapezoidal prism.
Examples on Trapezoidal Prism
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Example 1: Sandy is setting up a tent that is in the shape of a trapezoidal prism with dimensions as height as 4 units, lengths of the trapezoid as 4 units and 8 units, and length of the prism as 10 units. How many cubic feet of space are there in her tent?
Solution: To find the space in her tent, we need to find the volume of the tent. Given is h = 4, a = 8, b = 4, and I = 10
The volume of a trapezoidal prism = A × I cubic units
We need to find the area of the trapezoid. the formula is
Area (A) = ½ × h × (a + b)
A = ½ × 4 × (8 + 4)
A = 2 × 12
A = 24 square feet
Let us find the volume now.
Volume of a trapezoidal prism = A × I
V = 24 × 10
V = 240 cubic feet
Therefore, the number of cubic feet of space in sandy's tent is 240 cubic feet.
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Example 2: Find the surface area of the given trapezoidal prism with height as 3 units, lengths of the bases as 4.5 units, and 6 units, lateral length as 5, and sides of the prism as 2.5 units.
Solution: Let us add all the values that we have from the given image into the formula.
Surface Area of a Trapezoidal Prism = h (b + d) + l (a + b + c + d)
A = 3 (4.5 + 6) + 5 (4.5 + 2.5 + 6 + 2.5)
A = 3 × 10.5 + 5 × 15.5
A = 31.5 + 77.5
A = 109 units2
Therefore, the surface area of the given trapezoidal prism is 109 units2
FAQs on Trapezoidal Prism
What is a Trapezoidal Prism?
A trapezoidal prism is a 3D shape with two trapezoids as its base that is being joined by four rectangles. A trapezoidal prism was given its name since it is made up of trapezoids. A trapezoidal prism has six faces, eight vertices, and 12 edges. One of the box noticeable example of a trapezoidal prism that we see in daily life is fire brick.
What is the Formula to Calculate the Volume of a Trapezoidal Prism?
To find the volume of a trapezoidal prism, we need to first find the area of one trapezoid. The formula to calculate the volume of a trapezoidal prism is:
Volume of a Trapezoidal Prism = A × I
Area (A) = ½ × h × (a + b) or ½ h(b1+ b2)
Where h is the height of trapezoidal, l is the height of the prism, a and b are the lengths of the top and bottom of a trapezoidal prism
What is the Formula to Calculate the Surface Area of a Trapezoidal Prism?
The formula to calculate the surface area of a trapezoidal prism is:
Surface Area of a Trapezoidal Prism = h (b + d) + l (a + b + c + d)
where h is the height, b and d are the lengths of the base, a + b + c + d is the perimeter, and l is the lateral surface area.
What is the Net of a Trapezoidal Prism?
The net of a trapezoidal prism is that it consists of two trapezoids and four rectangles. When the trapezoidal prism is flattened, we can see these two images clearly.
How do you Find the Height of a Trapezoidal Prism?
In order to find the height of a trapezoidal prism, we need to find the area of one of the trapezoids. Since the prism has two trapezoids, to calculate the volume we need to find the height of one of the trapezoids using this formula:
Area (A) = ½ × h × (a + b)
where A is the area, h is the height, a and b are the lengths of the base trapezoids
Why is the Trapezoidal Prism a 3D Figure?
The 3D figure of a trapezoid is called a trapezoidal prism since these are figures that have a length, width, and depth. The edges of the prism is where the faces meet, and the vertices of the prism are the corners where three or more surfaces meet.