Math Problem Statement

What are the names of these polygons? (Image contains shapes labeled a, b, c, d with respective polygon sides to identify.)

Solution

Let’s analyze the image and identify the names of the polygons:

Explanation:

  • Polygon naming depends on the number of sides and whether the shape is convex or concave. Here's the analysis:
  1. a) The polygon has 7 sides.

    • Name: Heptagon (a convex shape with seven sides).
  2. b) The polygon has 9 sides.

    • Name: Nonagon (a convex shape with nine sides).
  3. c) This polygon has 5 sides, but it is concave (one angle points inward).

    • Name: Concave Pentagon.
  4. d) This polygon has 6 sides and is also concave.

    • Name: Concave Hexagon.

Would you like further clarification or details on polygons?

5 Related Questions:

  1. What is the difference between convex and concave polygons?
  2. How do you calculate the sum of the interior angles of a polygon?
  3. What are some real-world examples of polygons?
  4. How can you classify a polygon by symmetry?
  5. What are regular vs. irregular polygons?

Tip:

For any polygon, the formula for the sum of interior angles is (n2)×180°(n-2) \times 180°, where nn is the number of sides.

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Math Problem Analysis

Mathematical Concepts

Polygon classification
Convex and concave polygons
Properties of polygons

Formulas

Sum of interior angles = (n-2) × 180°

Theorems

Polygon side-count theorem for naming polygons

Suitable Grade Level

Grades 6-8