Answer:
Explanation:
To find the volume of the composite figure, we can break it down into smaller rectangular prisms and then sum their volumes.
Here's how the figure can be divided:
The larger rectangular prism at the bottom with dimensions 12 yards by 8 yards by 4 yards.
The smaller rectangular prism on top of the larger one with dimensions 12 yards by 8 yards by 2 yards.
The two smaller rectangular prisms on each side of the larger one, each with dimensions 2 yards by 8 yards by 4 yards.
We'll find the volume of each of these components and then add them together.
Volume of the larger rectangular prism:
Volume = Length x Width x Height
Volume = 12 yards x 8 yards x 4 yards
Volume = 384 cubic yards
Volume of the smaller rectangular prism on top:
Volume = Length x Width x Height
Volume = 12 yards x 8 yards x 2 yards
Volume = 192 cubic yards
Volume of one of the smaller rectangular prisms on the side:
Volume = Length x Width x Height
Volume = 2 yards x 8 yards x 4 yards
Volume = 64 cubic yards
Since there are two of these prisms on each side, we need to multiply the volume by 2:
Total volume of both smaller prisms on the sides = 2 x 64 cubic yards = 128 cubic yards
Now, add the volumes of all the components together to find the total volume of the composite figure:
Total Volume = 384 cubic yards (large bottom prism) + 192 cubic yards (small top prism) + 128 cubic yards (small side prisms) = 704 cubic yards
So, the volume of the composite figure is 704 cubic yards.