Tetrahedra in the solid geometry is called a polyhedron composed of four triangular faces. The tetrahedron has 6 edges and 4 faces and vertices.

If all the faces of the tetrahedron are right triangles, the tetrahedron, and he called right.

Total surface area of ​​any polyhedron including a tetrahedron can be calculated from the area of ​​its faces.

instructions

1

To find the total surface area of ​​the tetrahedron, it is necessary to calculate the triangle area of ​​his face.

If the triangle is equilateral, then its area is

S = 3 * 4 / a ?, where a -? A rib of the tetrahedron,

then the surface area of ​​the tetrahedron is given by

S =? 3 * a ?.

2

If the tetrahedron is rectangular, ie.e. all of the plane angles at one of its vertices are straight, the area of ​​three of its faces are right triangles can be calculated by the formula

S = a * b * 1/2,

S = a * c * 1/2,

S = b * c * 1/2,

the third face area can be calculated by one of the general formulas for the triangles, such as the Heron's formula

S = (p * (p - d) * (p - e) * (p - f))?, Where p = (d + e + f) / 2 - half-perimeter of the triangle.

3

In general, any tetrahedron area can be calculated by using Heron's formula for calculating the area of ​​each of its faces.