Math Problem Statement

Determine whether or not the figure is a polygon. If it is a polygon, decide if it is concave or convex.

Solution

The given figure is a polygon because it is a closed figure made up of straight line segments.

Next, we need to determine whether it is concave or convex:

  • Convex Polygon: All interior angles are less than 180°, and no line segment between any two points of the polygon passes outside of it.
  • Concave Polygon: At least one interior angle is greater than 180°, and a line segment between two points of the polygon can pass outside the polygon.

In this case, the polygon has an angle greater than 180°, as indicated by the inward "dent" in the figure. Therefore, the polygon is concave.

Answer:

  • Concave polygon

Would you like further explanation or have any questions?

Here are 5 follow-up questions based on this topic:

  1. What is the difference between concave and convex polygons?
  2. Can a polygon with all equal sides and angles be concave?
  3. How do you calculate the sum of interior angles of any polygon?
  4. What is the minimum number of sides a polygon must have to be concave?
  5. Can a triangle ever be concave?

Tip: For any polygon, if you can draw at least one diagonal that lies outside the polygon, it is concave!

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Math Problem Analysis

Mathematical Concepts

Polygons
Concave and Convex Polygons
Geometry

Formulas

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Theorems

Polygon classification by angles

Suitable Grade Level

Grades 6-8