To find the volume of this composite figure, we need to break it down into two rectangular prisms and find the volume of each before adding them together.

Step-by-Step Solution

1. Identify the two rectangular prisms:

   • Prism 1 (Vertical Section):
     • Dimensions: 2 ft (width) × 4 ft (depth) × 8 ft (height)
   • Prism 2 (Horizontal Section):
     • Dimensions: 5 ft (width) × 2 ft (depth) × 2 ft (height)

2. Calculate the Volume of Each Prism:

   • Volume of Prism 1:
     $V_1 = \text{width} \times \text{depth} \times \text{height} = 2 \, \text{ft} \times 4 \, \text{ft} \times 8 \, \text{ft} = 64 \, \text{cubic feet}$

   • Volume of Prism 2:
     $V_2 = \text{width} \times \text{depth} \times \text{height} = 5 \, \text{ft} \times 2 \, \text{ft} \times 2 \, \text{ft} = 20 \, \text{cubic feet}$

3. Add the Volumes:

   • Total Volume = $V_1 + V_2 = 64 + 20 = 84 \, \text{cubic feet}$

Answer:

The volume of the figure is $\mathbf{84}$ cubic feet.

Would you like further details or have any questions?

Here are some related questions for further practice:

1. What is the surface area of this composite figure?
2. How would the volume change if the height of the vertical section increased by 2 feet?
3. If the horizontal section was extended to a width of 6 feet, what would the new volume be?
4. How would the volume change if all dimensions were doubled?
5. What would be the volume if the depth of both sections was reduced by half?

Tip: When dealing with composite figures, break them into simple shapes, calculate individual volumes, and then sum them for the total volume.