Section 1
Decomposing Composite Figures
Property
The volume of a composite figure can be found by decomposing it into non-overlapping rectangular prisms and adding their individual volumes.
Examples
- An L-shaped figure can be decomposed into two rectangular prisms. The total volume is the sum of the volumes of the two smaller prisms.
- A T-shaped figure can be split into a horizontal prism and a vertical prism. Its total volume is found by adding the volumes of these two parts.
- A figure shaped like steps can be split into multiple rectangular prisms stacked on top of each other. The total volume is the sum of the volumes of all the steps.
Explanation
A composite figure is a three-dimensional shape made by combining two or more simpler shapes. To find the volume of a composite figure, we first break it down, or decompose it, into familiar shapes like rectangular prisms. After identifying the individual prisms, the next step is to find the volume of each one separately. The total volume of the composite figure is simply the sum of the volumes of all the individual prisms.