To calculate the area of one triangular lateral face of a triangular prism (or pyramid), you can use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base is 14 and the height is 8.7. Thus, the area of one triangular face is:
\[ \text{Area} = \frac{1}{2} \times 14 \times 8.7 \]
Calculating this step-by-step:
- Calculate \( \frac{1}{2} \times 14 = 7 \).
- Now, multiply by 8.7:
\[ 7 \times 8.7 = 60.9 \]
So, the area of one triangular lateral face is 60.9 square units.
Next, to find the total area of all three triangular lateral faces, multiply the area of one face by 3:
\[ \text{Total Area} = 3 \times 60.9 = 182.7 \]
Thus, the area of the three triangular lateral faces is 182.7 square units.