QQuestionMathematics
QuestionMathematics
Polygon ABCDE has 5 sides. Which is a correct description of the polygon?
A. It is a concave pentagon because segment AE would extend into the inside of the polygon, and it has five sides.
B. It is a convex hexagon because it has six sides and none of the sides would extend into the inside of the polygon.
C. It is a concave hexagon because segment AE would extend into the inside of the polygon, and it has six sides.
D. It is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the definition of a polygon
- A polygon is a closed plane figure with straight sides - The number of sides determines the polygon's name - A pentagon has 5 sides - A hexagon has 6 sides
Step 3:: Analyze the number of sides
- The problem states the polygon has 5 sides - This means it is a pentagon, not a hexagon
Step 4:: Understand concave vs. convex polygons
- A convex polygon has no interior angles greater than 180° - In a convex polygon, all vertices point outward - If any line segment between two vertices extends inside the polygon, it is concave
Step 5:: Examine the description of segment AE
- The problem states segment AE would extend into the inside of the polygon - This means the polygon is concave, not convex
Step 6:: Combine the information
- 5 sides = pentagon - Segment AE extends inside = concave
Final Answer
It is a concave pentagon because segment AE would extend into the inside of the polygon, and it has five sides.
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