Question 23A right pyramid has regular octagon $ABCDEFGH$ with side length $1$ as its base and apex $V.$ Segments $\overline{AV}$ and $\overline{DV}$ are perpendicular. What is the square of the height of the pyramid?$1$$\dfrac{1 + \sqrt2}{2}$$\sqrt2$$\dfrac{3}{2}$$\dfrac{2 + \sqrt2}{3}$