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All You Need to Know About a Tetrahedron?

Tetrahedron: A type of triangle-based 3-dimensional prism with four triangles forming the faces of the shape is called a tetrahedron. Sometimes it is also referred to as a triangular pyramid with 4 faces, 6 edges, and 4 vertices.

Understanding the basic tetrahedron shape

Generally speaking, any polyhedron with four faces is called a tetrahedron. The faces are triangular. The term is most probably used for a regular shape of a polyhedron of four sides.

Tetrahedron
Tetrahedron

Definition of tetrahedron

This is a sort of pyramid, that is one of the various types of a polyhedron having a flat polygonal base and triangle-shaped faces joining the base with the same common point. In the case of a tetrahedron, the base is a triangle and hence the figure gets its name as a “triangular pyramid”.

The figure is a convex polyhedron with two nets and any triangular face can be taken as a base as all the faces are regular.

Properties of a tetrahedron

  • The figure is made by compiling four congruent triangles together. Thus it has 4 faces, 6 edges, and 4 vertices.
  • Any of the four faces can be taken as the base.

Describing different types of tetrahedrons

The tetrahedrons are of different types are followings:

  1. Regular tetrahedrons have all the dimensions equal: The sides of all the triangles are congruent to each other and identical in measurements. In other words, the regular tetrahedron has equilateral triangles as its faces.
  2. Non-regular or irregular tetrahedrons: Any pyramid whose base with sides of different lengths is an irregular tetrahedron. The base has unequal sides of the base triangular face is either a scalene triangle or it may also be an isosceles triangle with two of its sides equal.
  3. Right tetrahedrons: The tetrahedron with a base angle same as the measurement of a right angle i.e., 90 degrees is a right tetrahedron.

Explaining the net of a Tetrahedron

A net of the tetrahedron is formed when its surface is spread out flat giving a complete view of each triangular face of the figure just like the 2- d figures. For various solids, the net pattern is different. For finding the net pattern of a solid take note of the following points:

  • The pyramid and the net must have equal faces.
  • The shapes of the faces of the pyramid should be the same as the shapes of the faces in the net.
  • The respective folds forming the pyramid should be considered and it should be assured that all the sides fit together properly.

Calculating the volumes and surface areas

VOLUME: The formula of Volume of a tetrahedron = ⅓ × Base Area × Height, i.e., one-third of the product of the area of base and height gives the volume of the respective figure.

SURFACE AREA: The relation for the surface area of any tetrahedron = (Base area) + ½ × Perimeter × (Slant length), i.e., the sum of the base area with half the product of perimeter and slant height of the figure. For any regular, this calculation is simple. First, find the measurements of the base and the height of any triangle.

Then find the product of those and get half of it. This area is of the triangle. Now, multiply this area by four to get the total surface area. For an irregular tetrahedron, the area of every triangle is calculated individually, using the area formula and then all the areas are added together to get the final surface area.

Cuemath explains the topic of such polyhedrons with examples and applications. In geometry, we have a large number of such concepts, one of which is Dodecahedron. It is a 12-sided flat polyhedron with 12 faces, 30 edges, and 20 vertices. It has regular pentagons on its face and is also known as a dodecahedron.

Cuemath experts explain such geometrical concepts in an efficient manner making the topics simple to understand and use.

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