Given cube $PQRS-TUVW$. It has the length of the side is $3\sqrt3 cm$. What is the distance between $PRW$ plane and $QVT$ plane?
Attempt:
Cz there's no information about the labelling, i consider $PQRS$ is a clockwise direction of the cube's label and $TUVW$ as well.
The distance between $PRW$ amd $QVT$ plane is of course the same as the half of the diagonal space of the cube.
So, to find the half of the diagonal space, i use the area formula of the triangle $PQR$.
$\begin{align} A. PQR &= A. PQR\\ \frac 12*(3\sqrt3)^2 &= \frac 12* 3 \sqrt6 * x\\ x &= \frac 32 \sqrt6 \end{align}$
And $x$ is the distance, approximately $x=3.67$. But, my friends found it $3$. Which one is true?
Btw here is my sketch
Since $(PWR)||(TQV)$ and $US\perp(PWR),$ we obtain that the needed distance is $$\frac{1}{3}US=\frac{1}{3}\sqrt{3(3\sqrt3)^2}=3.$$