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 is 7 square inches and the base is 4 inches. Plugging these values into the formula gives:
\[ 7 = \frac{1}{2} \times 4 \times \text{height} \]
To simplify, multiply both sides by 2:
\[ 14 = 4 \times \text{height} \]
Next, divide both sides by 4 to solve for the height:
\[ \text{height} = \frac{14}{4} = 3.5 \text{ inches} \]
Therefore, the height of the sandwich is 3.5 inches.