{"uid":"cap_Q8gtQ6unRS3DRCcqGnokK","slug":"polygon-area-perimeter-centroid-calculator-dbd53281","name":"Polygon Area, Perimeter & Centroid Calculator","description":"Area (shoelace formula), perimeter and centroid of a simple polygon given its vertices in order. Vertices are treated as a closed ring (last connects to first).","url":"https://geometry.openverbs.com/v1/polygon","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":["points"],"properties":{"points":{"type":"array","items":{"type":"array","items":{"type":"number"},"maxItems":2,"minItems":2},"maxItems":10000,"minItems":3,"description":"Vertices as [x, y] pairs, in order."}},"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_THvRGI6od90snfswvMFlx","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 shoelace formula), perimeter, and centroid of a simple polygon given an ordered list of 2D vertices.","exampleAgentPrompt":"Calculate the area, perimeter, and centroid of a polygon with vertices at [0,0], [4,0], [4,3], [0,3] — treating them as a closed ring.","exampleUseCases":[{"title":"Land parcel area estimation","prompt":"I have a land parcel with corners at coordinates [0,0], [100,0], [110,80], [50,120], [0,90] — can you calculate its total area, perimeter, and center point?"},{"title":"Floor plan polygon metrics","prompt":"Here are the vertices of an irregular room floor plan in meters: [1,1], [5,1], [6,4], [4,6], [1,5]. What's the area, perimeter, and centroid of this shape?"},{"title":"Game zone boundary calculation","prompt":"I'm designing a game map zone with boundary points [200,150], [400,100], [500,300], [450,500], [250,480], [100,350]. What's the area and center of this polygon?"}],"resultDescription":"Returns the computed area of the polygon (using the shoelace formula), its perimeter (sum of all edge lengths), and the coordinates of its centroid (geometric center), given the ordered list of 2D vertex coordinates.","failureModes":["Fewer than 3 vertices provided — returns validation error","Malformed coordinate pairs (not exactly 2 numbers) — schema validation failure","More than 10,000 vertices submitted — exceeds maxItems limit","Self-intersecting polygon passed — result may be geometrically incorrect without an error","Non-numeric coordinate values — type validation error","Payment not provided or insufficient — 402 Payment Required response"],"whenToPreferThis":"Use this endpoint when you need all three core polygon metrics — area, perimeter, and centroid — computed in a single call from an ordered vertex list. Prefer it over manual computation when dealing with arbitrary irregular polygons (not rectangles or triangles, which have sibling endpoints). Ideal when vertices are already in coordinate form and you need a fast, reliable geometric result without setting up a local math library.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T12:34:22.609Z","isFirstParty":false}