By decomposing the figure into a rectangular prism and a triangular prism, calculating their individual volumes, and adding them up, we found that the total volume of the figure is 304 cubic centimeters.
1. Identify and decompose the solid:
The figure is a combination of two basic solids:
A rectangular prism: This forms the base of the figure, with dimensions 8 cm (length) x 14 cm (width) x 2 cm (height).
A triangular prism: This sits on top of the rectangular prism, sharing the same 8 cm x 2 cm base. Its triangular face has dimensions 8 cm (base) and 20 cm (height).
2. Calculate the volume of each solid:
Rectangular prism volume:
= lwh = 8 cm x 14 cm x 2 cm = 224 cm³
Triangular prism volume:
= ½bh = ½ * 8 cm * 20 cm = 80 cm³
3. Calculate the total volume:
The total volume of the figure is the sum of the volumes of the two individual solids:
= 224 cm³ + 80 cm³ = 304 cm³
Therefore, the volume of the figure is 304 cubic centimeters.