69 Given a cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ with edge length $a$, and $A C_{1}$ is its space diagonal, then among all sections perpendicular to $A C_{1}$, the maximum area is
A. $\frac{\sqrt{3}}{2} a^{2}$
B. $\frac{3 \sqrt{3}}{4} a^{2}$
C. $\sqrt{3} a^{2}$
D. $\sqrt{2} a^{2}$
69 C. The area of $\triangle A B_{1} D_{1}$ is $\sqrt{3} a^{2}$, and it is the largest cross-section perpendicular to $A C_{1}$.