MathNet 2020 — Math Olympiad Vault — Part 05 Question 5

In parallelepiped $ABCDA_1B_1C_1D_1$, the angles $A_1AD,A_1AB,DAB$ are all 60°. Given $C_1A_1=\sqrt7$, $C_1B=\sqrt{13}$ and $C_1D=\sqrt{19}$ centimeters, find the distance from $A$ to plane $A_1BD$.