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Tetrahedron
A tetrahedron is a threedimensional shape that has four triangular faces. One of the triangles is considered as the base and the other three triangles together form the pyramid. The tetrahedron is a type of pyramid, which is a polyhedron with triangular faces connecting the base to a common point and a flat polygon base. It has a triangular base and thus it is also referred to as a triangular pyramid. Let us learn more about the tetrahedron shape, a regular tetrahedron, tetrahedron angles, and so on in this article.
1.  Tetrahedron Definition 
2.  Net of a Tetrahedron 
3.  Tetrahedron Properties 
4.  Surface Area of Tetrahedron 
5.  Volume of Tetrahedron 
6.  FAQs on Tetrahedron 
Tetrahedron Definition
A tetrahedron is also known as a triangular pyramid whose base is also a triangle. A regular tetrahedron has equilateral triangles, therefore, all its interior angles measure 60°. The interior angles of a tetrahedron in each plane add up to 180° as they are triangular. Observe the tetrahedron given below to understand its shape.
Tetrahedron Net
In geometry, a net can be defined as a twodimensional shape which when folded in a certain manner produces a threedimensional shape. A tetrahedron is a 3D shape that can be formed using a geometric net. Take a sheet of paper. Observe the two distinct tetrahedron nets shown below. Copy this on the sheet of paper. Cut it along the border and fold it as directed in the figure. The folded paper forms a tetrahedron.
Properties of Tetrahedron
A tetrahedron is a threedimensional shape that is characterized by some distinct properties. The figure given below shows the faces, edges, and vertices of a tetrahedron.
Tetrahedron Faces Edges Vertices
A tetrahedron is a polyhedron with 4 faces, 6 edges, and 4 vertices, in which all the faces are triangles. Observe the tetrahedron given below to see its faces, vertices, and edges.
The following are the properties of a tetrahedron which help us identify the shape easily.
 It has 4 faces, 6 edges, and 4 vertices (corners).
 In a regular tetrahedron, all four vertices are equidistant from each other.
 It has 6 planes of symmetry.
 Unlike other platonic solids, it has no parallel faces.
 A regular tetrahedron has four equilateral triangles as its faces.
Surface Area of Tetrahedron
The surface area of a tetrahedron is defined as the total area or region covered by all the faces of the shape. It is expressed in square units, like m^{2}, cm^{2}, in^{2}, ft^{2}, yd^{2}, etc. A tetrahedron can have two types of surface areas:
 Lateral Surface Area of Tetrahedron
 Total Surface Area of Tetrahedron
Lateral Surface Area of a Tetrahedron
The lateral surface area of a tetrahedron is defined as the surface area of the lateral or the slant faces of a tetrahedron. The formula to calculate the lateral surface area of a regular tetrahedron is given as,
LSA of Regular Tetrahedron = Sum of 3 congruent equilateral triangles, i.e., lateral faces
= 3 × (√3)/4 a^{2}
where 'a' is the side length of a regular tetrahedron.
Total Surface Area of a Tetrahedron
The total surface area of a tetrahedron is defined as the surface area of all the faces of a tetrahedron. The formula to calculate the total surface area of a regular tetrahedron is given as,
TSA of Regular Tetrahedron = Sum of 4 congruent equilateral triangles, i.e., all its faces
= 4 × (√3)/4 a^{2} = √3 a^{2}
where 'a' is the side length of the regular tetrahedron.
Volume of Tetrahedron
The volume of a tetrahedron is defined as the total space occupied by it in a threedimensional plane. The formula to calculate the tetrahedron volume is given as,
The volume of regular tetrahedron = (1/3) × area of the base × height = (1/3) × (√3)/4 × a^{2} × (√2)/(√3) a
= (√2/12) a^{3}
where 'a' is the side length of the regular tetrahedron. The volume of a tetrahedron is expressed in cubic units.
Tetrahedron Angles
In a regular tetrahedron, all the faces are equilateral triangles. Therefore, all the interior angles of a tetrahedron are 60° each. The sum of the face angles for 3 faces of a tetrahedron, that meet at any vertex is 180°.
Important Notes on Tetrahedron
 The 5 platonic solids can be listed as tetrahedron, cube, octahedron, icosahedron, and dodecahedron.
 A tetrahedron is a triangular pyramid with all 4 faces as triangles.
 A tetrahedron has 4 faces, 6 edges, and 4 corners.
☛ Related Topics
Tetrahedron Examples

Example 1: Two congruent tetrahedrons are stuck together along their base to form a triangular bipyramid. How many faces, edges, and vertices does this bipyramid have?
Solution:
If we open the triangular bipyramid in order to see its net, it will be similar to what is shown in the following figure:
This shows that the triangular bipyramid has 6 triangular faces, 9 edges, and 5 vertices.

Example 2: State true or false with respect to a tetrahedron.
a.) A tetrahedron is a polyhedron with 4 faces, 6 edges, and 4 vertices.
b.) A tetrahedron has no parallel faces.
Solution:
a.) True, a tetrahedron is a polyhedron with 4 faces, 6 edges, and 4 vertices.
b.) True, a tetrahedron has no parallel faces.

Example 3: Each edge of a regular tetrahedron is 6 units. Find its total surface area.
Solution:
The total surface area of a regular tetrahedron is:
Total Surface Area = √3a^{2}
Substituting 'a' = 6, we get:
Total Surface Area = √3 × 6^{2}
= √3 × 6 × 6= 62.35
Therefore, the total surface area of the tetrahedron is 62.35 square units.
FAQs on Tetrahedron
What is a Tetrahedron?
A tetrahedron is a platonic solid which has 4 triangular faces, 6 edges, and 4 corners. It is also referred to as a 'Triangular Pyramid' because the base of a tetrahedron is a triangle. A tetrahedron is different from a square pyramid, which has a square base.
What are the Properties of a Tetrahedron?
The properties of a tetrahedron are:
 It has 4 faces, 6 edges, and 4 corners.
 All four vertices are equally distant from each other in a regular tetrahedron.
 Unlike other platonic solids, it has no parallel faces.
 A regular tetrahedron has all its faces as equilateral triangles.
 It has 6 planes of symmetry.
Is a Tetrahedron a Pyramid?
Yes, a tetrahedron is a type of pyramid because a pyramid is a polyhedron for which the base is always a polygon and the other lateral faces are triangles. Since a tetrahedron has a triangular base and all its faces are triangles, it is known as a triangular pyramid.
Is a Square Based Pyramid a Tetrahedron?
No, a squarebased pyramid is not a tetrahedron. A squarebased pyramid has a square base and all its other faces are triangles, whereas, a tetrahedron has a triangular base and all its faces are equilateral triangles. Thus, a squarebased pyramid is not a tetrahedron.
What is the Base of a Tetrahedron Shape?
A tetrahedron is a figure with 4 triangular faces, therefore, the base of a tetrahedron is also a triangle.
How to Find the Volume of a Tetrahedron?
The volume of a tetrahedron can be calculated using the formula, Volume of tetrahedron = (1/6√2) a^{3}, where 'a' is the side length of the tetrahedron. The volume of a tetrahedron is expressed in terms of cubic units.
What is a Regular Tetrahedron Shape?
In a regular tetrahedron, all the faces are equilateral triangles. All the edges of a regular tetrahedron are also equal in length.
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