[ [ Regular Tetrahedron ]

Find the area of the complete surface of a regular tetrahedron with an edge equal to $a$.

#
Let $A B C D$ be a regular tetrahedron with edge $a, S$ - the area of the total surface. All faces of the tetrahedron are equal equilateral triangles with side $a$. Therefore,

$$
S=4 S_{\triangle A B C}=4 \cdot \frac{a^{2} \sqrt{3}}{4}=a 2 \sqrt{3}
$$

Answer

$a 2 \sqrt{3}$.