The area \( A \) of a right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Plugging in the values for the base and height:
\[ A = \frac{1}{2} \times 10 , \text{cm} \times 7.4 , \text{cm} \]
\[ A = \frac{1}{2} \times 74 , \text{cm}^2 = 37 , \text{cm}^2 \]
Thus, the area of the triangle is \( 37 \) square centimeters.