The tetrahedron in Greek means "tetrahedron." This geometric figure has four faces, four vertices and six edges. Faces are triangles. In fact, the tetrahedron is a triangular pyramid. The first mention of polyhedra appeared long before the existence of Plato.
Today we’ll talk about the elements and properties of the tetrahedron, and also find out the formulas for finding the area, volume and other parameters of these elements.
Tetrahedron elements
A segment released from any vertex of a tetrahedron and dropped to the intersection point of the medians of a face that is opposite is called the median.
The height of the polygon is a normal segment, omitted from the vertex opposite.
A bimedian is a line connecting the centers of crossed edges.
Tetrahedron properties
1) Parallel planes that pass through two intersecting ribs form the described parallelepiped.
2) A distinctive feature of the tetrahedron is that the medians and bimedians of the figure meet at the same point. It is important that the latter divides the medians in a 3: 1 ratio, and the bimedians in half.
3) The plane divides the tetrahedron into two equal parts in volume if it passes through the middle of two intersecting edges.
Types of Tetrahedron
The species diversity of the figure is quite wide. The tetrahedron may be:
- regular, that is, at the base of an equilateral triangle;
- equilateral, in which all faces are the same in length;
- orthocentric when the heights have a common intersection point;
- rectangular if the flat angles at the vertex are normal;
- proportionate, all bi heights are equal;
- wireframe, if there is a sphere that touches the ribs;
- eccentric, that is, the segments dropped from the vertex to the center of the inscribed circle of the opposite face have a common intersection point; this point is called the center of gravity of the tetrahedron.
Let us dwell in detail on the regular tetrahedron, whose properties are practically the same.
Based on the name, it can be understood that it is called so because the faces are regular triangles. All edges of this figure are congruent in length, and faces in area. A regular tetrahedron is one of five similar polyhedra.
Quadrangle Formulas
The height of the tetrahedron is equal to the product of the root of 2/3 and the length of the rib.
The volume of the tetrahedron is the same as the volume of the pyramid: divide the square root of 2 by 12 and multiply by the length of the edge in the cube.
The remaining formulas for calculating the area and radii of circles are presented above.