8. Areas and polygons

More graph objects

Two types of graph objects allow you to shade regions of a graph: areas and polygons. As with other objects, you may drag additional instances of an area onto the graph as long as the palette icon remains in color, and you can always remove objects by dragging all control points off the graph.

Working with areas

Areas appear on the palette as a control point within a shaded box, and they can be used to fill in any region regardless of its shape. Wherever you place the point on the graph, the filled-in region will extend beyond that point until it reaches another graphical object or the edge of the graph.

Suppose the following graph represents a painting on a canvas. Use the black point (plus symbol) to draw the line bisecting the barn door, then use the purple area (diamond symbol) to shade the barn door. Afterward, use the tan area (rectangle symbol) to shade the roof of the barn and the blue area (circle symbol) to shade the sky.

Note: You will not be graded on any changes you make to the graph.

Door divider

Barn doors

Roof

Sky

CANVAS HEIGHT (Inches)

CANVAS WIDTH (Inches)

More about areas

Selecting anywhere in the shaded region other than the control point will sometimes reveal the area of the shaded region. As with other tool tips, it will not take the graph axes' units into account. Areas are graded based on the shape of the entire filled-in area, not on the specific location of the point defining the area. (There will often be multiple correct placements for the point defining the area.)

By selecting the filled-in regions on the graph, you can determine that the area of the canvas covered by the barn door is equal to ___________ square inches.

Which of the following statements are true regarding areas?Check all that apply.

Changing the position of other objects on the graph may change the shape of the possible regions you may fill.

Each palette icon will always allow you to drag only one fill area onto the graph.

Areas can be used to shade a region of any shape.

Working with polygons

Once you have placed a polygon on the graph, you can adjust its shape by selecting and dragging any of the polygon's endpoints to another snap point. As with lines and curves, you can also select the entire polygon to change its location on the graph without changing its shape. In some cases, you can view the area and perimeter by selecting anywhere within the polygon other than the endpoints.

Use the purple rectangle (diamond symbols) to again shade the barn doors, then use the tan triangle (rectangle symbols) to shade the roof.

Roof

Barn doors

CANVAS HEIGHT (Inches)

CANVAS WIDTH (Inches)

True or False: The endpoints of a polygon must conform to snap points, whereas the edges of an area are not confined by snap points.

True

False