To calculate the area of the shaded face of the triangular prism, we focus on the triangular shape where the shading is applied. The dimensions provided are:

• One side of the triangle is 18 cm (base of the triangle),
• The height from the base to the top of the triangle is 6 cm.

Since the shaded face is a triangle, we can use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Substituting the values:

$\text{Area} = \frac{1}{2} \times 18 \, \text{cm} \times 6 \, \text{cm} = \frac{1}{2} \times 108 = 54 \, \text{cm}^2$

Thus, the area of the shaded face is 54 cm².

Would you like any further details on this solution, or do you have any other questions?

Here are some related questions to explore:

1. How would the area change if the height of the triangle were different?
2. What other types of prisms use similar methods to calculate surface areas?
3. How do we calculate the total surface area of a triangular prism?
4. What is the significance of the length of the prism in surface area calculations?
5. How can you find the volume of a triangular prism?

Tip: Always ensure the height is perpendicular to the base when calculating the area of a triangle!