"use strict";

function round2(x) { return Math.round(x * 100) / 100; }

function heronArea(a, b, c) {
  const s = (a + b + c) / 2;
  const inner = s * (s - a) * (s - b) * (s - c);
  if (inner <= 0) throw new Error("sides do not form a valid triangle");
  return Math.sqrt(inner);
}

module.exports = {
  slug: "triangle-area-heron",
  title: "Triangle area by Heron's formula",
  deck_category: "geometry",
  description: "Computes the area of a triangle from its three side lengths using Heron's formula.",
  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: [],
  sources: [
    { kind: "edition_page", value: "Coxeter, H.S.M. Introduction to Geometry, 2nd ed. Wiley, 1969, section 1.3.", title: "Introduction to Geometry, 2nd ed., Heron's formula", publisher: "Wiley", retrieved_utc: "2026-09-30T19:46:00Z", note: "Standard geometry reference for Heron's formula (attributed to Heron of Alexandria, Metrica)." }
  ],
  disclaimer: null,
  questionText(inputs) {
    return `What is the area of a triangle with sides ${inputs.a}, ${inputs.b}, and ${inputs.c}, using Heron's formula?`;
  },
  run(inputs) {
    const { a, b, c } = inputs || {};
    for (const [name, v] of Object.entries({ a, b, c })) {
      if (typeof v !== "number" || v <= 0) throw new Error(`${name} must be a positive number`);
    }
    const area = round2(heronArea(a, b, c));
    return { answer: `${area.toFixed(2)}`, values: { area } };
  },
  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."
    }
  ]
};