Question

what type of polygon is shown?

convex heptagon
concave heptagon
concave octagon
convex octagon

Explanation:

Count the number of vertices and sides

$$ \text{Vertices counted on the polygon: } 7 $$

$$ \text{Sides counted on the polygon: } 7 $$

$$ \text{A polygon with 7 sides is a heptagon.} $$

Determine if the polygon is convex or concave

$$ \text{At least one interior angle is greater than } 180^\circ \text{ (pointing inward).} $$

$$ \text{A diagonal can be drawn outside the polygon.} $$

$$ \text{Therefore, the polygon is concave.} $$

Identify the correct classification

$$ \text{Classification: concave heptagon} $$

Answer:

• convex heptagon
• concave heptagon (Correct answer)
• concave octagon
• convex octagon