user: I have a set of vertices: [[1,2],[3,4],[1,4],[3,7]], and I'm curious about the area that these points, when connected in order, would enclose to form a polygon. Could you calculate the area of this polygon for me?

Available functions:
name: convert_coordinates
description: Converts a list of tuples into a list of lists.
parameters: type: dict
properties: coordinates: type: array
items: type: tuple
items: type: float
description: A single coordinate represented by a tuple (x, y).
description: The coordinates to be converted, where each coordinate is a tuple (x, y).
required: coordinates
name: polygon_area
description: Calculate the area of a polygon given its vertices using the shoelace formula.
parameters: type: dict
properties: vertices: type: array
items: type: array
items: type: float
minItems: 2
maxItems: 2
description: A single vertex represented by a 2 element list [x, y].
description: The vertices of the polygon, where each vertex is a 2 element list [x, y].
required: vertices
name: validate_polygon
description: Checks if the given vertices form a valid polygon.
parameters: type: dict
properties: vertices: type: array
items: type: array
items: type: float
description: A single vertex represented by a 2 element list [x, y].
description: The vertices of the polygon, where each vertex is a 2 element list [x, y].
required: vertices