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:
- What is the difference between concave and convex polygons?
- Can a polygon with all equal sides and angles be concave?
- How do you calculate the sum of interior angles of any polygon?
- What is the minimum number of sides a polygon must have to be concave?
- 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