# Triangle Properties Calculator (Heron's Formula)

> Triangle Properties Calculator (Heron's Formula) is a paid API for AI agents from geometry.openverbs.com, paid per call via x402, $0.004/call, status unknown (last checked 2026-09-14).

Computes the area (via Heron's formula), perimeter, and all three interior angles of a triangle given its three side lengths, rejecting invalid triangles with a 400 error.

## Facts

- Endpoint: POST https://geometry.openverbs.com/v1/triangle
- Price: $0.004/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/triangle-properties-calculator-heron-s-formula-52a4e3aa
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_KvpeRPY_KZIx-rg-mJYCZ

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability triangle-properties-calculator-heron-s-formula-52a4e3aa -d '<json body>'
```

Example prompt: What's the area, perimeter, and all three interior angles of a triangle with sides 7, 10, and 12?

## When to prefer this

Use this endpoint when you have all three side lengths of a triangle and need area, perimeter, and/or interior angles without requiring coordinates. Prefer this over polygon endpoints when the shape is specifically a triangle. It's ideal when you want automatic validation of the triangle inequality as part of the workflow.

## Known failure modes

- Triangle inequality violation (e.g. sides 1, 2, 10) returns 400 Bad Request
- Any side length of zero or negative returns 400 due to exclusiveMinimum:0 constraint
- Missing required fields a, b, or c returns 400
- Non-numeric side values return a validation error

## How this service works

Area (Heron's formula), perimeter and interior angles of a triangle from its three side lengths. Sides that violate the triangle inequality are rejected as a clean 400.

## Output

Returns the triangle's area computed via Heron's formula, its perimeter (sum of all three sides), and the three interior angles in degrees. If the provided sides violate the triangle inequality (i.e., no valid triangle can be formed), the endpoint returns a 400 error.

## Request schema (JSON Schema)

```json
{
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "type": "object",
 "properties": {
  "input": {
   "type": "object",
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "type": "string",
     "enum": [
      "POST"
     ]
    },
    "bodyType": {
     "type": "string",
     "enum": [
      "json",
      "form-data",
      "text"
     ]
    },
    "body": {
     "type": "object",
     "properties": {
      "a": {
       "type": "number",
       "exclusiveMinimum": 0,
       "description": "Side a."
      },
      "b": {
       "type": "number",
       "exclusiveMinimum": 0,
       "description": "Side b."
      },
      "c": {
       "type": "number",
       "exclusiveMinimum": 0,
       "description": "Side c."
      }
     },
     "required": [
      "a",
      "b",
      "c"
     ],
     "additionalProperties": false
    }
   },
   "required": [
    "type",
    "method",
    "bodyType",
    "body"
   ],
   "additionalProperties": false
  }
 },
 "required": [
  "input"
 ]
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/triangle-properties-calculator-heron-s-formula-52a4e3aa/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from geometry.openverbs.com](https://www.zero.xyz/host/geometry.openverbs.com/llms.txt)