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.
Do not write an equation yet. Shake the figure first.
Push the top edge sideways
The silhouette and perimeter change, but a fixed base and height pin the area in place.
Play the reversal slowly
Now move the same pieces step by step and prove that the pattern you touched was not an accident.
A slanted parallelogram with base b and height h. Its area?
Return to the exact question
Find the area of a slanted parallelogram with base b and height h — using only cut-and-slide.
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
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