How to find the area of a tetrahedron

A tetrahedron in solid geometry is called a polyhedron, which consists of four triangular faces. The tetrahedron has 6 edges and 4 faces, and vertices. If the tetrahedron all faces are right triangles, then the tetrahedron is regular. The surface area of any polyhedron including a tetrahedron can be calculatedknowing the area of its faces.

Instruction

1. To find the surface area of the tetrahedron, it is necessary to calculate the area of a triangle which constitutes its face.
   
   If the triangle is equilateral, its area is equal to
   
   S = √3 * 4 / a2, where a is an edge of a tetrahedron
   
   then the surface area of the tetrahedron is given by
   
   S = √3 * a2.
2. If the tetrahedron is rectangular, i.e. all the flat corners with one of its vertices are straight, square, three faces are rectangular triangles can be calculated by the formula
   
   S = a * b *1/2,
   
   S = a * c *1/2,
   
   S = b * c *1/2,
   
   the area of the third face can be calculated by one of General formulas for triangles, for example, by Heron's formula
   
   S = √(p * (p - d) * (p - e) * (p - f)), where p = (d + e + f)/2 – properiter triangle.
3. In General, the area of each tetrahedron can be calculated using Heron's formula to calculate the area of each face.