The problem involves finding the value of $n$, the length of a triangular prism, given the volume and other dimensions.

Formula for the volume of a triangular prism:

$V = \text{Base Area} \times \text{Height (or length, } n\text{)}$

1. Base Area: The base is a triangle with dimensions:

   • Base = 14 yards
   • Height = 10 yards The area of the triangle is: $\text{Base Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 14 \times 10 = 70 \text{ square yards.}$

2. Volume of the prism: 1,050 cubic yards. Using the volume formula: $V = \text{Base Area} \times n \implies 1,050 = 70 \times n$

3. Solve for $n$: $n = \frac{1,050}{70} = 15 \text{ yards.}$

Final Answer:

$n = 15 \text{ yards.}$

Would you like me to explain any step in detail or explore related concepts?

Here are 5 related questions to deepen your understanding:

1. How is the volume of other 3D shapes, such as a cylinder or cone, calculated?
2. How do you find the area of a triangle if only its sides are given (Heron’s formula)?
3. What happens to the volume if the length of the prism doubles?
4. Can this method be applied to non-rectangular prisms, and how does it change?
5. How does unit conversion (e.g., yards to meters) affect the calculation of volume?

Tip: Always check the units for consistency (e.g., cubic yards for volume, square yards for area) to avoid calculation errors!