To calculate the area of the shaded triangular face of the prism, follow these steps:

Steps:

1. Identify the given dimensions:

   • The dimensions of the triangular face are:
     • Base $b = 13 \, \text{cm}$,
     • Height $h = 8 \, \text{cm}$.

2. Formula for the area of a triangle: $A = \frac{1}{2} \times \text{base} \times \text{height}$

3. Substitute the values: $A = \frac{1}{2} \times 13 \times 8$

4. Calculate the area: $A = \frac{1}{2} \times 104 = 52 \, \text{cm}^2$

Final Answer:

The area of the shaded face is 52 cm².

Would you like a detailed breakdown or additional help?

5 Related Questions:

1. How do you calculate the total surface area of the prism using all its faces?
2. How can the volume of this triangular prism be determined?
3. What is the relationship between the prism’s height and the base area in finding its volume?
4. How does changing the dimensions of the triangle affect its area?
5. What are the properties of triangular prisms compared to rectangular ones?

Tip:

Always ensure the base and height are perpendicular when calculating the area of a triangle!