The mass of the paper with shaded area is calculated using the formula:
\[
\text{Mass of shaded area} = \text{Total mass} \times \text{Drape coefficient}.
\]
Substitute the given values:
\[
\text{Mass of shaded area} = 3.0 \, \text{g} \times 0.7 = 2.1 \, \text{g}.
\]
Final Answer:
\[
\boxed{2.1}.
\]