{"uid":"cap_-Qi-pFknUw102_vRTOYvG","slug":"forgemesh-geometry-api-643f82ab","name":"ForgeMesh Geometry API","description":"Geometry API: exact area, perimeter, volume, surface area, and diagonals for circles, rectangles, triangles (Heron's or base-height), spheres, cylinders, cones, cubes, and rectangular prisms — from structured dimensions. Validates the triangle inequality. For CAD, construction, education, and design agents.","url":"https://x402.forgemesh.io/geometry","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"a":{"type":"string"},"b":{"type":"string"},"c":{"type":"string"},"base":{"type":"string"},"side":{"type":"string"},"shape":{"type":"string","description":"circle|rectangle|triangle|sphere|cylinder|cone|cube|rectangular_prism"},"width":{"type":"string"},"height":{"type":"string"},"length":{"type":"string"},"radius":{"type":"string"}}},"responseSchema":{"type":"json","example":{"shape":"sphere","volume":523.598776,"surface_area":314.159265}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.002","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":"$0.002/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.002","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.002","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_njbkVQmsSSQlOAeScBFhu","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.002","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes exact area, perimeter, volume, surface area, and diagonals for 2D and 3D geometric shapes from structured dimension inputs, with triangle inequality validation.","exampleAgentPrompt":"What's the volume and surface area of a cylinder with radius 4 and height 10? Also give me the area of its circular base.","exampleUseCases":null,"resultDescription":"Returns exact numeric values for the relevant geometric properties of the specified shape — such as area, perimeter, volume, surface area, and diagonals — based on the shape type and provided dimensions. For triangles, also validates the triangle inequality.","failureModes":["Missing required dimensions for the specified shape returns an error","Invalid shape type string returns an unrecognized shape error","Triangle sides that violate the triangle inequality return a validation failure","Non-numeric string values for dimension fields cause parsing errors","Omitting the 'shape' field results in an unprocessable request"],"whenToPreferThis":"Use this endpoint when you need mathematically exact geometric computations for standard 2D or 3D shapes without implementing formulas yourself — especially in CAD, construction planning, educational tools, or design workflows where precision matters. Prefer this over general-purpose math APIs when dealing specifically with geometric shapes and needing multiple properties (area + perimeter + diagonal) in a single call.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-13T18:33:57.508Z","isFirstParty":false}