Question 23
A 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?
(A) $1$ \quad (B) $\frac{1+\sqrt{2}}{2}$ \quad (C) $\sqrt{2}$ \quad (D) $\frac{3}{2}$ \quad (E) $\frac{2+\sqrt{2}}{3}$
(A) $1$ \quad (B) $\frac{1+\sqrt{2}}{2}$ \quad (C) $\sqrt{2}$ \quad (D) $\frac{3}{2}$ \quad (E) $\frac{2+\sqrt{2}}{3}$