A tetrahedron in stereometry is a polyhedron that consists of four triangular faces. The tetrahedron has 6 edges and 4 faces and peaks.
If for a tetrahedron all faces are regular triangles, then the tetrahedron itself is called regular.
The area of the total surface of any polyhedron, including a tetrahedron, can be calculated, knowing the areas of its faces.
To find the area of the total surface of the tetrahedron, it is necessary to calculate the area of the triangle of its component face.
If the triangle is equilateral, its area is
S =? 3 * 4 / a ?, where a is the edge of the tetrahedron,
Then the surface area of the tetrahedron is found from formula
S =? 3 * a ?.
In the case when the tetrahedron is rectangular, that is,Ie, all planar angles at one of its vertices are straight, then the areas of its three faces being rectangular triangles can be calculated from 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 the general formulas for triangles, for example, by Heron's formula
S =? (P * (p - d) * (p - e) * (p - f)), where p = (d + e + f) / 2 is the semiperimeter of the triangle.
In general, the area of any tetrahedron can be calculated using the Heron formula to calculate the areas of each of its faces.