Area vs Perimeter

Same perimeter can fence different areas

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About This Practice

Does the same length of fencing always enclose the same area? The perimeter stays fixed while you move 1 unit between length and width; the rectangle stretches or squashes and its area changes on the spot. Hunt for the largest area you can enclose and notice which length–width ratio wins.

Keep the perimeter fixed while stretching a rectangle longer or wider, and watch its area change in real time. Hunt for the largest area you can fence and discover: the closer to a square, the bigger the area.

MediumEstimated Time: 15minarea vs perimetersame perimeter different areamaximize areafixed perimeterfencing problem

How to Play

  1. Read the readout: perimeter = 2 × (length + width) — it never changes as you adjust.
  2. Tap “length +1 · width −1” or the reverse and watch the rectangle and the area equation react.
  3. Follow the area bar: did this adjustment grow the area or shrink it?
  4. Keep adjusting until you find the largest area, then read the conclusion.
  5. Tap “New Perimeter” and test whether your discovery still holds.

Learning Objectives

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