{"uid":"cap_KvpeRPY_KZIx-rg-mJYCZ","slug":"triangle-properties-calculator-heron-s-formula-52a4e3aa","name":"Triangle Properties Calculator (Heron's Formula)","description":"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.","url":"https://geometry.openverbs.com/v1/triangle","method":"POST","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method","bodyType","body"],"properties":{"body":{"type":"object","required":["a","b","c"],"properties":{"a":{"type":"number","description":"Side a.","exclusiveMinimum":0},"b":{"type":"number","description":"Side b.","exclusiveMinimum":0},"c":{"type":"number","description":"Side c.","exclusiveMinimum":0}},"additionalProperties":false},"type":{"type":"string","const":"http"},"method":{"enum":["POST"],"type":"string"},"bodyType":{"enum":["json","form-data","text"],"type":"string"}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.004","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.004/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.004","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.004","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_dIp6nKUSXP9D7-_DvGymu","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.004","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"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.","exampleAgentPrompt":"What's the area, perimeter, and all three interior angles of a triangle with sides 7, 10, and 12?","exampleUseCases":[{"title":"Verify triangle validity and area","prompt":"I have a triangle with sides 5, 12, and 13 — can you tell me its area, perimeter, and interior angles?"},{"title":"Engineering cross-section measurement","prompt":"Calculate the area and angles of a triangular cross-section with side lengths 8.5, 6.2, and 9.1."},{"title":"Detect degenerate triangle in user input","prompt":"A user entered side lengths 1, 2, and 10 for a triangle — are those valid, and if so what's the area and perimeter?"}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T18:41:22.451Z","isFirstParty":false}