Question

hi

Answer 1

You have a regular tetrahedron here, where all 4 sides are equilateral triangles with side lengths of 4. Now, the area of one these triangles is given by \[{\sqrt{3} \over 4}\cdot s^2={\sqrt{3} \over4}\cdot 4^2=4\sqrt{3}\]

Hence, the lateral area is given by \[4\sqrt3 \cdot (3)\]Since you have 3 sides that aren't a "base."

The total area is given by \[4\sqrt3 \cdot(4)\] Since there are 4 total sides.

And the volume is given by the formula \[{\sqrt2 \over 12}\cdot s^3={\sqrt2 \over 12}\cdot 4^3\]

Answer 2

That is correct.

Answer 3

\[\Large {\sqrt2 \over 12}\cdot 4^3\]Which simplifies to \[\Large {16 \sqrt2 \over 3}\]