A Slanted Parallelogram — Cut and Slide into a Rectangle
A slanted parallelogram looks awkward — until you cut the triangle off one end and slide it to the other, making a clean rectangle: base × height at a glance.
Problem
Find the area of a slanted parallelogram with base b and height h — using only cut-and-slide.
Cut · rotate · rearrange
Press Play or move Next one step at a time. Follow the pieces until the answer becomes visible. (Arrow keys and Space also work.)
A slanted parallelogram with base b and height h. Its area?
Why this approach works
Cut a right-triangle off the left with a vertical line, then translate it to the empty notch on the right. Because opposite sides are equal and parallel, it fits exactly, forming a rectangle. Nothing is added or lost, so the area is base × height = b × h — the slant is irrelevant.
Proof
Cutting the left triangle and translating it right yields a rectangle; area is preserved, so the parallelogram equals base × height.
Try it yourself
Imagine shearing it further: the cut triangle just gets longer and thinner, but it still slides into the same b × h rectangle.
Related mathematics
Beyond MathVoyage
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