Given $A(0,0,0),B(a,0,0),C(a,a,0),D(0,a,0),D'(0,a,a)$. Choose $E(\lambda,0,0)$ and $F(a,\mu,0)$. Calculating the condition $\mu=\frac{2a\lambda}{a+\lambda}$. Equation of the plane $(DD'E\ :\ ax+\lambda(y-a)=0$, normal vector of this plane $(a,\lambda,0)$. Equation of the plane $(DD'F\ :\ x(\mu-a)-a(y-a)=0$, normal vector of this plane $(\mu-a,-a,0)$. The angle $\alpha$ formed by the planes: $\cos \alpha=\frac{1}{\sqrt{2}}$. The plane, through point $D'$ and $\bot EF$ has equation $(a-\lambda)x+\mu y=a \mu$ and cuts $EF$ in the point $S(\frac{2a^{2}\lambda}{a^{2}+\lambda^{2}},\frac{2a\lambda^{2}}{a^{2}+\lambda^{2}},0)$. Distance $D'S=\sqrt{2} \cdot a$.