Source: https://guthlabs.ai/docs/instruments/2d-shape-area-perimeter-calculator/mechanism/

instrument mechanism / verified-clean

# 2D Shape Area/Perimeter Calculator mechanism

The inspectable method record for 2D Shape Area/Perimeter Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/2d-shape-area-perimeter-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/2d-shape-area-perimeter-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/2d-shape-area-perimeter-calculator/qualification/>)

## 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`