lesson
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Imagine building a giant toy castle out of colorful wooden blocks.
When you put simple box shapes together to make a new tricky shape, we call it a compound shape.
📊Interactive diagram
How can we find the total space inside this shape without losing count?
Slicing into Simple Boxes
We can draw an imaginary cut line to split the shape into two easy box shapes called rectangular prisms.
📊Interactive diagram
Once we split the shape, we count the cubes in each box and add them together.
The tall blue box has 3 cubes, and the orange box has 1 cube. 3+1=4 total cubes!
This rule is the Additive Property of volume. For non-overlapping sections, the total volume is Vtotal=V1+V2+⋯+Vn.
Instead of counting individual cubes, find each piece's volume with the Prism Volume Formula: V=l×w×h or V=Abase×h, where l is length, w is width, and h is height.
When dividing solids, look for Consistent Shared Dimensions—such as a single width or depth that stays the same across each sub-prism.
Deducing Missing Dimensions is often necessary when an edge is unlabelled. Find the unknown length by comparing parallel sides: lmissing=ltotal−lgiven