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Do you know, the word, "Tetrahedron" can be split into two words? One is the "Tetra" and the other is the "hedron". Both are from ancient Greek times, tetra means four and hedron means faces. In simple words, we are talking about a geometrical figure that has four faces in a three-dimensional plane. Therefore, we dedicated this resource to the regular tetrahedron.
What is a Tetrahedron?
As mentioned before, a tetrahedron is a three-dimensional shape that contains four faces but what kind of faces? Are they rectangles? Are they squares? We want you to find it out, below is the image of a tetrahedron, take your time and consider one of the faces and figure out what is the shape of the face is?
Yes, absolutely! It is a triangle. Therefore, a tetrahedron is a three-dimensional figure that has four faces and each face is a triangle.
Regular Tetrahedron
However, the topic of this resource talks about a regular tetrahedron, let's talk about it. One thing is for sure, it will be a tetrahedron but if you see the word, "regular" attached to it, that means all faces of the tetrahedron will have the same dimensions. In simple words, a regular tetrahedron is a regular polyhedron composed of 4 equally sized equilateral triangles. Furthermore, a regular tetrahedron is also known as a triangular pyramid which is another topic that deserves its own resource, let's stick to tetrahedron for now.
Unfold of a Regular Tetrahedron
To reveal more secrets of a regular tetrahedron, we need to unfold it. This will give us a lot of information about its characteristics and we could use the unfolded figure to make the formula for the calculation of surface area. Without any further ado, let's open it.
Of course, since all faces are triangles, we will end up with a triangle too. The unfolded figure looks like a big triangle and inside of that triangle is a small triangle that is fitted perfectly.
Characteristics of the Tetrahedron
The unfolded figure of the tetrahedron gave a lot of information including characteristics. Let's take a look at it.
The first thing that you note is the faces. Take your time and count how many faces are there and tally it with our answer.
Number of faces: 4.
Vertix means the joining of two endpoints that are responsible for connecting a geometrical figure. This is found using the 3-dimensional figure, not the unfolded one.
Number of vertices: 4.
Number of edges: 6.
Number of concurrent edges at a vertex: 3.
Surface Area of a Regular Tetrahedron
With the help of the unfolded tetrahedron figure, we can find the right formula for calculating the surface area. Surface area means the space occupied by the boundary of the shape.
Where, a is the edge of a tetrahedron.
Volume of a Regular Tetrahedron
The volume of a regular tetrahedron means that the total space occupied by the whole regular tetrahedron. Below is the formula for the calculation of the volume of a regular tetrahedron.
Where, a is the edge of a tetrahedron.
Example
Calculate the suface area and volume of a regular tetrahedron with an edge of 5 cm.
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Hello,
the solution of Exercise No.3 …volume 1 = 30m3
and the last fraction is 30/0.24 = 125