To find the area of the new room, we need to simplify the expression \(1.75s(2s + 3)\).
We will distribute \(1.75s\) to both terms inside the parentheses:
\[ 1.75s(2s + 3) = 1.75s \cdot 2s + 1.75s \cdot 3 \]
Calculating each part, we find:
\[ 1.75s \cdot 2s = 3.5s^2 \]
\[ 1.75s \cdot 3 = 5.25s \]
Now, combining these results, we have:
\[ 1.75s(2s + 3) = 3.5s^2 + 5.25s \]
Thus, the expression that represents the area of the new room is:
\[ \boxed{3.5s^2 + 5.25s} \]