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IBM

MCP Math Server

by IBM

geom_polygon_area

Calculate polygon area using the Shoelace formula by providing vertex coordinates as input.

Instructions

Calculate the area of a polygon using the Shoelace formula (Domain: geometry, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
verticesYes
Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations provided, the description carries the full burden of behavioral disclosure. It states the calculation method (Shoelace formula) but lacks critical details: it doesn't specify input format (e.g., coordinate pairs as strings), error handling (e.g., for invalid polygons), performance characteristics, or output format. This leaves significant gaps in understanding how the tool behaves beyond its basic purpose.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose and method. There is no wasted language or redundancy, making it efficient for quick comprehension. The structure is clear, with the core action ('Calculate the area') presented immediately.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's complexity (mathematical calculation with a single but semantically rich parameter), no annotations, and no output schema, the description is incomplete. It lacks details on input format, output structure, error conditions, and usage context relative to siblings like 'geom_triangle_area'. This makes it inadequate for reliable agent invocation without additional assumptions or trial-and-error.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate for undocumented parameters. It mentions 'vertices' implicitly but provides no details on their format (e.g., 'x,y' strings), ordering (clockwise/counterclockwise), or constraints (minimum vertices, non-self-intersecting). This fails to add meaningful semantics beyond the bare schema, leaving the single parameter poorly explained.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Calculate the area of a polygon' with a specific method ('using the Shoelace formula'). It distinguishes itself from sibling tools like 'geom_triangle_area' by handling general polygons. However, it doesn't explicitly contrast with 'geom_triangle_area' or other geometry tools, keeping it from a perfect score.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides minimal usage guidance: it mentions the domain (geometry) and category (general), but offers no explicit when-to-use instructions, prerequisites, or alternatives. For example, it doesn't clarify when to use this versus 'geom_triangle_area' for triangles or other polygon-related tools, leaving the agent with little contextual direction.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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