Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.
Choose the informal argument that supports a geometric formula
Problem
Explain the formula \(A~=~bh\) for a parallelogram using an area-preserving cut-and-move argument. Identify the relocated piece, the resulting familiar shape, and the dimensions that remain \(b\) and \(h\).
An area argument should preserve the region while converting it into a shape with a familiar formula. We’ll distinguish perpendicular height from the slanted side, identify a movable overhang, track the base and height through the rearrangement, and connect the unchanged area to the resulting dimensions.
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