To create simple area (polygon) features in Global Mapper, open the 
Digitizer Toolset and chose an option from the Create section:
Create Area Feature
Create Rectangle/ Square Area Feature
Create Circle/ Ellipse Area FeatureAdditional Area Feature Creation Tools
Alternatively, when the Digitizer Tool is active, new area features can be created by right-clicking, and selecting the Create Area/ Polygon Features menu to access the options below. These options are also available from the top-level digitizer menu.
Tips for creating Arc, Circular, Elliptical, Rectangular, and Square area and line features
To begin creating the feature, (except the rectangular/ square option where the coordinates are manually entered), click and hold the left mouse button at the center of the feature, then drag it until it is of the desired shape.
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For Circular/ Elliptical features and Arcs, the default shape follows a circle and holding down the SHIFT key while dragging will result in an ellipse.
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For Rectangular/ Square features, the default shape is a rectangle and holding down the SHIFT key will force the dragged shape to be square. By default, the start point is treated as the top left corner of the feature. To treat it as the center instead, hold down the 'T' key when left clicking to start the shape.
Once the shape is finished, release the left mouse button and the Modify Feature Info dialog will appear allowing you to setup the label, classification, drawing style, and attribution for the new feature. See Editing Feature Attributes and Drawing Styles for more details.
After the shape is created, the Digitizer Tool will remain in the selected shape creation mode. Left click to start drawing a new shape, right-click to choose a different mode, or press ESC to return to the main Digitizer tool.
The following options are available:
Create
Area Feature
Create Range Ring(s)\ Ellipse(s)
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Create New
Line with Dist/ Bearing/ COGO Input
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Create Grid
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Create
Coverage Area (Concave Hull) for Selected/ Loaded Features
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Create Buffers Around Selected Feature(s)
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Create New Features from Selected Lines
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- Create Arc Area
Create
Circular/ Elliptical Area
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Create Rectangular/ Square
Area
- Create Rotated Rectangular Area (3 Point Draw)
- Create Rectangular/ Square Area (specify Coordinates)
- Create Square Areas of Fixed Ground Area
For automated digitizing, see Create Area Features from Equal Values, Vectorize Raster, and the Global Mapper Insight and Learning Engine™ (Beta) .