A prism is a solid figure with flat faces, 2 identical bases, and the same cross-section all the way around. The name of a prism is determined by its 2 bases, which can be triangles, rectangles, or any other polygon. A prism with triangular bases, for example, is known as a triangular prism. It includes 2 triangular bases and 3 rectangular lateral faces. In this article, we will learn more about the triangular prism and its properties.
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What is a Triangular Prism?
We’ve all seen a triangular shape in physics, which is used to prove relative density as well as light reflection and scattering. This triangular shape is commonly referred to as a triangular prism. A triangular prism is a three-dimensional piece with three rectangular faces, 2 triangular faces, and a well-defined flat side. From the front, the prism appears to be a perfect triangle.
A triangular prism is a three-dimensional polyhedron with two triangular faces and three rectangular faces. The two triangular faces are congruent to each other, while the three lateral faces which are in the shape of rectangles are also congruent to each other. A triangular prism, therefore, has 5 faces, 9 edges, and 6 vertices. Examine the image of a triangular prism below, where l denotes the prism’s length, h denotes the base triangle’s height, and b denotes the bottom edge of the base triangle.
Triangular Prism Properties
The properties of a triangular prism make it easy to identify. A triangular prism has the following properties:
- It includes 9 edges, 5 faces, and 6 vertices
- It has 2 triangular bases and 3 rectangular sides.
- If the triangular bases are equilateral and the other faces are squares rather than rectangles, the triangular prism is considered to be semiregular.
Types of Triangular prisms
Triangular prism classification based on intersecting faces
The bases and lateral faces of triangular prisms could be categorized based on how they intersect or meet. A right triangular prism has bases that are perpendicular to the lateral faces and meet at right angles. It is otherwise an oblique triangular prism.
Regular and irregular triangular prisms
Triangular prisms are also classified according to the type of triangle that forms their base. A regular prism is described as a prism with regular polygon bases. As a result, if the triangular prism’s bases are equilateral triangles, it is a regular triangular prism. Otherwise, it is irregular. A regular triangular prism is frequently assumed to be a right triangular prism.
Right Triangular Prism
A right triangular prism has triangular faces that are perpendicular to the three rectangular faces. In other words, because the angle formed by the intersection of the rectangle and triangle faces must be 90 degrees, the triangular faces are perpendicular to the lateral rectangular faces.
Volume and Surface Area of Triangular Prism
The triangle prism contains two crucial formulas. These are the formulas for prism volume and prism area. A prism’s volume is the space inside the triangular prism. A triangular prism’s surface area is the amount of covered space on its outside surface. We need to have the prism’s height, side length, and base length for these calculations.
The volume of the Triangular Prism Formula
The volume of a triangular prism is equivalent to the product of the triangular base’s area and the prism’s height. Thus:
The volume of the Prism = Area of the Base × Height of the prism
Mathematically, V = 1/2 × b × h × l, where:
V : The volume of the prism
b: Base length
h: Height of the triangle
l: Length of the prism
The surface area of the Triangular Prism Formula
A triangular prism’s surface area is calculated by adding the lateral surface area and base areas of both triangle bases. Thus,
The surface area of the triangular prism = Lateral Area + 2 times the triangular base area
Mathematically, S.A = P × H + 2A, where:
S.A: The surface area of the prism
A: Area of the base
P: The perimeter of the base
H: Height of the prism
Read more >> What is a Scalene Triangle? Definition, Properties, and Formulas
What are real-world examples of triangular prisms?
It’s great if you know what a triangular prism is, but you also have to be able to recognize one when you see one. Take a look at this list of places where you can find triangular prisms in everyday life the next time you are outside:
- Roofs of houses: When you look at the roofs of houses, you will notice that the majority of them are triangular prisms. This is because it has a strong roof structure, and rain runs through the sides and onto the ground. If houses had flat roofs, rain would collect on top and leak inside.
- Tents are also another excellent example of a triangular prism. They’re exactly the shape we’re looking for. Tents, like roofs, are shaped this way to protect us from rain and other environmental factors. It also indicates that there will be plenty of space on the floor for people to sleep.
- Chocolate: If you have ever seen a Toblerone bar, you’ll notice that the package is shaped clearly like a triangular prism. Furthermore, all of the pieces inside are shaped like tiny, thin triangular prisms.
Frequently Asked Questions on Triangular Prism
What exactly is a triangular prism?
A triangular prism is a three-dimensional polyhedron with 5 faces, 6 edges, and 9 vertices. It has triangular bases and rectangular sides.
How many faces, edges, and vertices are in a triangular prism?
A triangular prism has five faces, three rectangular and two triangular, nine vertices, and six edges.
What is the distinction between triangular and rectangular prisms?
A triangular prism has triangle-shaped bases, whereas a rectangular prism has rectangle-shaped bases.
Hope that the above article helps you grasp the perfect answer to the question “What is a triangular prism?”.
