The area \( A \) of a right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Given that the base is 10 centimeters and the height is 7.4 centimeters, we can substitute these values into the formula:
\[ A = \frac{1}{2} \times 10 , \text{cm} \times 7.4 , \text{cm} \]
Calculating this:
\[ A = \frac{1}{2} \times 10 \times 7.4 = 5 \times 7.4 = 37 , \text{square centimeters} \]
Therefore, the area of the triangle is 37 square centimeters.