2D Shape Area/Perimeter Calculator mechanism

Model scope

The honest label is empty and should state that the current specification is incomplete: only circle area, sector area, and polygon shoelace area are explicitly supplied. The advertised support for rectangle, regular polygon, trapezoid, ellipse, sector/segment, and all perimeter outputs requires additional formulas, input constraints, angle-unit handling, and an ellipse-perimeter approximation policy.

• The specification does not provide a perimeter formula for any shape, although perimeter is listed as an output.
• The shoelace formula computes polygon area only; polygon perimeter requires summing Euclidean distances between consecutive vertices, including the closing edge.
• Rectangle formulas are missing: area = width × height and perimeter = 2(width + height).
• Trapezoid formulas are missing: area = 1/2(a + b)h and perimeter = a + b + c + d.
• Regular-polygon formulas and the required inputs, such as side length or apothem, are missing.
• Ellipse area is missing: A = πab. Ellipse perimeter has no general elementary exact formula, so an approximation method and its accuracy must be specified.

Units and conventions

• All linear dimensions must use the same unit; areas are in the corresponding squared unit and perimeters in the corresponding linear unit.
• The circle and sector formulas require a nonnegative radius.
• Sector and segment angles must be explicitly identified as radians or converted from degrees before use; the formula A = 1/2r²θ assumes radians.
• For shoelace polygons, vertices must be ordered around the boundary, clockwise or counterclockwise, with the closing edge from the last vertex to the first.
• π is assumed to be the mathematical constant π; displayed decimal precision must be specified.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "shape": "circle",
    "radius": 5,
    "length_unit": "cm"
  },
  "expected_outputs": {
    "area": 78.53981633974483,
    "perimeter": 31.41592653589793,
    "area_unit": "cm²",
    "perimeter_unit": "cm"
  },
  "working": "Area = πr² = π × 5² = 25π = 78.53981633974483 cm². Perimeter = 2πr = 2 × π × 5 = 10π = 31.41592653589793 cm."
}

Failure boundary

• Division by zero is not inherent in the listed formulas, but any future formulas using an apothem, height, radius, or other denominator must reject zero denominators.
• Negative radii, negative lengths, invalid polygon vertex lists, fewer than three polygon vertices, and non-finite numeric inputs require validation.
• Self-intersecting polygon vertices can produce an algebraic shoelace result that is not the intended geometric area; this case needs an explicit policy.
• A sector angle outside the valid range for the intended sector representation, such as an angle greater than 360 degrees, needs validation or a defined interpretation.
• Ellipse perimeter requires an approximation or numerical method; labeling it as exact without qualification would be misleading.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json