# Polygons and Other Interiors

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Polygons and other interiors are Sketchpad objects that define a region of a plane. Interiors give your sketches substance and color, and allow you to measure the areas and perimeters of figures. Use the perimeter or circumference of an interior as a path on which to construct or animate points.

There are four kinds of interiors: polygons, circle interiors, arc sectors, and arc segments.

Polygon | Circle Interior | Arc Sector Interior | Arc Segment Interior

Polygons and interiors are path objects.

You can change the object properties, label properties, and display attributes of interiors.

| Construct an Interior

Use Construct | Polygon Interior to construct a polygon defined by three or more selected vertex points.
Use the Polygon tool to construct a polygon.
Use Construct | Circle Interior to construct the interior of each selected circle.
Use Construct | Arc Interior | Arc Sector to construct the sector interior of each selected arc. An arc sector is bounded by the arc and by the radii to the two endpoints of the arc.
Use Construct | Arc Interior | Arc Segment to construct the segment interior of each selected arc. An arc segment is bounded by the arc and by the chord connecting the endpoints of the arc.

| Use an Interior

• | Construct a point on an interior using the Point tool or the Construct | Point on Object command. Then animate the point around the interior or use the point as the driver for a locus.
• | Attach an independent point to the perimeter or circumference of the interior by using the Edit | Merge command.
• | Change an interior’s layer using Bring to Front or Send to Back from the Context menu.
• | Change the opacity of an interior using Edit | Properties | Opacity.

| Use a Polygon

Use a polygon in the same way as other interiors. In addition, there are some special ways in which you can use or change polygons.
• | Construct all the segment edges of a selected polygon by choosing Edit | Select Parents and then choosing Construct | Segments.
• | Construct a new polygon and its segment edges at the same time by using the Polygon and Edges tool.
• | Construct a polygon’s first intersection with a ray using Construct | First Intersection.
• | Crop a picture to a polygon using Edit | Crop Picture to Polygon, so that only the portion of the picture within the polygon is visible.
• | Create an angle marker by pressing the Marker tool on a vertex and dragging into the interior of the polygon.
Polygon Frame: A polygon can be displayed with or without a frame that shows its perimeter. The frame is an optional display attribute of the polygon. It does not represent the segment edges of the polygon: You cannot select an individual segment edge of the frame or perform any construction or measurement on the frame, except for constructions or measurements that apply to the polygon itself. To construct the midpoint of a segment edge or measure the length of a segment edge of the polygon, you must explicitly construct that segment edge.
Polygon Displayed Without Frame | Polygon Displayed With Frame
• | Show or hide the frame of the polygon using Edit | Properties | Opacity and changing the setting for Frame polygon perimeter.
To show only the frame, first show the frame and then set Opacity to 0%.
• | Change the width of the polygon’s frame using Display | Line Style.
• | Determine whether new polygons display their frames by choosing Edit | Preferences | Tools and changing the setting for Frame new polygon perimeters.

| Measure an Interior

Use the Measure menu to find:
• | the Perimeter of a polygon or an arc interior.
• | the Circumference of a circle interior.
• | the Radius of a circle interior or an arc interior.
• | the Arc Angle or Arc Length of an arc interior.