To calculate the volume of the given solid, we note that it is composed of two parts:

1. A rectangular prism at the bottom.
2. A triangular prism on top.

Step 1: Volume of the Rectangular Prism

The dimensions of the rectangular prism are:

• Length = 24 yards
• Width = 20 yards
• Height = 10 yards

The volume of a rectangular prism is given by: $V_{\text{rect}} = \text{Length} \times \text{Width} \times \text{Height}$ $V_{\text{rect}} = 24 \times 20 \times 10 = 4800 \, \text{yd}^3$

Step 2: Volume of the Triangular Prism

For the triangular prism, we first calculate the area of the triangular face. The dimensions of the triangle are:

• Base = 24 yards
• Height = 16 yards

The area of the triangular face is: $A_{\text{triangle}} = \frac{1}{2} \times \text{Base} \times \text{Height}$ $A_{\text{triangle}} = \frac{1}{2} \times 24 \times 16 = 192 \, \text{yd}^2$

The triangular prism extends for a width of 20 yards. Thus, the volume of the triangular prism is: $V_{\text{triangle}} = A_{\text{triangle}} \times \text{Width}$ $V_{\text{triangle}} = 192 \times 20 = 3840 \, \text{yd}^3$

Step 3: Total Volume

The total volume of the solid is the sum of the volumes of the rectangular and triangular prisms: $V_{\text{total}} = V_{\text{rect}} + V_{\text{triangle}}$ $V_{\text{total}} = 4800 + 3840 = 8640 \, \text{yd}^3$

Final Answer:

The total volume of the solid is: $\boxed{8640 \, \text{yd}^3}$

Would you like a breakdown of these steps or any clarifications?

Related Questions:

1. How is the surface area of this solid calculated?
2. What is the weight of the solid if the material density is given?
3. How would the volume change if the triangular prism's height was 20 yards instead of 16 yards?
4. Can you verify the volume using cross-sectional slicing methods?
5. What is the ratio of the triangular prism's volume to the rectangular prism's volume?

Tip:

Always double-check units and ensure that all dimensions align with the required calculations to avoid errors in mixed unit problems.