{
  "address": "a3eed12002999305f54f020739211ca4",
  "category": "other",
  "question": "What is the area of a triangle with sides 3, 4, and 5, using Heron's formula?",
  "answer": "6.00",
  "askedBy": {
    "kind": "guest",
    "display": "method deck",
    "stamped": false,
    "id": null
  },
  "answeredBy": "method",
  "madeAt": "2026-09-30T22:39:30.722Z",
  "validUntil": null,
  "validityClass": "forever",
  "sources": [
    {
      "label": "Introduction to Geometry, 2nd ed., Heron's formula",
      "url": null
    }
  ],
  "supersedes": null,
  "supersededBy": null,
  "isSeed": false,
  "seedSource": null,
  "seedAttribution": null,
  "duplicateOfQid": null,
  "publishedAt": null,
  "unpublishedAt": null,
  "voteCount": 0,
  "queuedForSubstrate": false,
  "answerMethod": "method",
  "unsourced": false,
  "source": {
    "kind": "edition_page",
    "value": "Coxeter, H.S.M. Introduction to Geometry, 2nd ed. Wiley, 1969, section 1.3.",
    "retrieved_utc": "2026-09-30T19:46:00Z"
  },
  "qsha256": "b77ffea1ceda3141f148bb15bd9de269d272e6345d4deb9fb300d863d4baf512",
  "runOne": null,
  "cardContractVersion": "card_contract/1",
  "deck_id": "method-deck",
  "deck_title": "Method Deck",
  "method": {
    "name": "Triangle area by Heron's formula",
    "version": "1",
    "source_url_or_file": "methods/triangle-area-heron.cjs",
    "sha256_of_method_file": "c4b4c18ad06ae7c0597b7d5c002933d31ee34f1978ede94a3555666570e4d7e0"
  },
  "receipt": {
    "inSubstrate": false,
    "local": true,
    "modelCallsAtMint": 0,
    "tokensAtMint": 0
  },
  "method_deck": {
    "inputs": [
      {
        "name": "a",
        "type": "number",
        "unit": "length units",
        "required": true,
        "description": "First side length.",
        "min": 0
      },
      {
        "name": "b",
        "type": "number",
        "unit": "length units",
        "required": true,
        "description": "Second side length.",
        "min": 0
      },
      {
        "name": "c",
        "type": "number",
        "unit": "length units",
        "required": true,
        "description": "Third side length.",
        "min": 0
      }
    ],
    "outputs": [
      {
        "name": "area",
        "unit": "square length units",
        "description": "Triangle area."
      }
    ],
    "steps": [
      "Compute the semiperimeter s = (a + b + c) / 2.",
      "Check the triangle inequality: s*(s-a)*(s-b)*(s-c) must be positive, otherwise the three lengths cannot form a triangle.",
      "area = sqrt( s*(s-a)*(s-b)*(s-c) ).",
      "Round to 2 decimals."
    ],
    "constants": [],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "a": 3,
          "b": 4,
          "c": 5
        },
        "expected": {
          "answer": "6.00"
        },
        "check": "A 3-4-5 triangle is a right triangle with legs 3 and 4, so its area is independently known to be (3*4)/2 = 6.00, matching Heron's formula's sqrt(6*3*2*1) = sqrt(36) = 6.00."
      },
      {
        "name": "test vector: isosceles triangle",
        "inputs": {
          "a": 5,
          "b": 5,
          "c": 6
        },
        "expected": {
          "answer": "12.00"
        },
        "check": "A 5-5-6 isosceles triangle splits into two 3-4-5 right triangles with base 6 and height 4, so its area is independently known to be (6*4)/2 = 12.00, matching Heron's formula's sqrt(8*3*3*2) = sqrt(144) = 12.00."
      }
    ],
    "disclaimer": null,
    "deck_category": "geometry"
  },
  "status": "minted",
  "kind": "method",
  "provenanceClass": "own_question",
  "provenance": {
    "schema": "card_provenance/2.0.0",
    "chain": [
      {
        "source": {
          "kind": "edition_page",
          "value": "Coxeter, H.S.M. Introduction to Geometry, 2nd ed. Wiley, 1969, section 1.3.",
          "retrieved_utc": "2026-09-30T19:46:00Z"
        },
        "sha256": "c7586e2fb189156b6b53d553561c630232038bcfe00b7de9da58a06caee1bcf3",
        "supersedes": null,
        "added_utc": "2026-09-30T22:39:30.722Z",
        "added_by": "method:Triangle area by Heron's formula",
        "why": "the method that computed this answer",
        "check": null,
        "status_label": "pending",
        "signature": null
      }
    ]
  }
}