To find the height of the triangular sandwich, we can use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
We know the area of the sandwich is 7 square inches and the base is 4 inches. Let's denote the height as \( h \). Plugging in the values we know:
\[ 7 = \frac{1}{2} \times 4 \times h \]
Solving for \( h \):
\[ 7 = 2h \]
\[ h = \frac{7}{2} = 3.5 \]
Thus, the height of the sandwich is 3.5 inches.