To find the area of the triangular lid of the box, you can use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Given the base of the triangle \( b = 7.5 \) cm and the height \( h = 4 \) cm, you can substitute these values into the formula:
\[ \text{Area} = \frac{1}{2} \times 7.5 , \text{cm} \times 4 , \text{cm} \]
Calculating this gives:
\[ \text{Area} = \frac{1}{2} \times 7.5 \times 4 = \frac{1}{2} \times 30 = 15 , \text{cm}^2 \]
Therefore, the area of the box lid is \( 15 , \text{cm}^2 \).