The diagram shows a prism with a rectangular base, $$\(A B F E\)$$. The cross-section, $$\(A B C D\)$$, is a trapezium with $$\(A D=B C\)$$. $$\(A B=8 \mathrm{~cm}, G H=5 \mathrm{~cm}, B F=12 \mathrm{~cm}\)$$ and angle $$\(A B C=70^{\circ}\)$$. The perpendicular from $$\(G\)$$ onto $$\(E F\)$$ meets $$\(E F\)$$ at $$\(X\)$$. Calculate $$\(A X\)$$. $$\[ A X= ....................................... \mathrm{cm} \]$$

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