regular triangular pyramid.

[123]

Hello,

Given a regular triangular pyramid. 
Find the volume of the pyramid and the total surface area.

if it's a regular triangular pyramid I think it means that is tetrahedron.
$\displaystyle V=\frac{\sqrt{2}}{12}a^3$
how find a?

 

[tkhunny]

Are you sure it isn't $\displaystyle \angle{D} = 60^{\circ}$?

 

[soroban]

$\displaystyle \text{No, }\angle SAC = 60^o.$

\(\displaystyle \angle D \:=\:\tan^{-1}(\sqrt{2}) \:\approx\:54.7^o\\)

 

[tkhunny]

Well, okay, but I'm still worried about the 30 shown in the original post.

 

[lookagain]

Hello,

Given a regular triangular pyramid. 
Find the volume of the pyramid and the total surface area.

It doesn't make sense to ask how many degrees are in the measure of angle D,
because it is not a unique angle. State the intended angle by angle SDO or
angle ODS.

The blue coloring at that corner (vertex) does not absolve the angle of being
properly labeled.