To find the area \( A \) of a triangle given two sides and the included angle, you can use the formula:
\[ A = \frac{1}{2}ab \sin(C) \]
where \( a \) and \( b \) are the lengths of the two sides, and \( C \) is the measure of the included angle.
Given:
- \( a = 9 \) cm
- \( b = 5 \) cm
- \( C = 40^\circ \)
First, we need to find \( \sin(40^\circ) \). Using a calculator, we find:
\[ \sin(40^\circ) \approx 0.6428 \]
Now, substituting the values into the area formula:
\[ A = \frac{1}{2} \times 9 , \text{cm} \times 5 , \text{cm} \times \sin(40^\circ) \] \[ A = \frac{1}{2} \times 9 \times 5 \times 0.6428 \] \[ A = \frac{45}{2} \times 0.6428 \] \[ A = 22.5 \times 0.6428 \approx 14.5 , \text{cm}^2 \]
Thus, rounding to the nearest tenth, the area of the triangle is:
\[ \boxed{14.5 , \text{cm}^2} \]