Question

use the polygon to the right to complete parts a and b.

(a) name the polygon. if the polygon is a quadrilateral, give its specific name.
(b) state whether or not the polygon is a regular polygon.

(a) what is the name of the polygon?
nonagon
rectangle
decagon
hexagon

(b) is the polygon regular or not regular?
not regular
regular

Explanation:

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<reasoning>

Count the sides of the polygon

To classify the polygon, we first count the number of its sides (or vertices). Looking at the shape in the upper right corner, we can count:

1. Top horizontal-ish side
2. Upper-right slanted side
3. Lower-right slanted side
4. Bottom horizontal-ish side
5. Lower-left slanted side
6. Upper-left slanted side

There are exactly 6 sides.

Classify the polygon by its sides

A polygon with 6 sides is defined as a hexagon.

• A nonagon has 9 sides.
• A rectangle is a specific 4-sided quadrilateral.
• A decagon has 10 sides.
• A hexagon has 6 sides.

Therefore, the correct choice for part (a) is Hexagon.

Analyze if the polygon is regular

A regular polygon must be both equilateral (all sides are equal in length) and equiangular (all interior angles are equal).
Looking closely at the given hexagon:

• The top and bottom horizontal sides are noticeably shorter than the slanted side segments.
• The interior angles are not all equal.

Since the side lengths and interior angles are not all congruent, the polygon is Not Regular.
</reasoning>

<answer>

Question 1

<mcq-option>(A) Nonagon</mcq-option>
<mcq-option>(B) Rectangle</mcq-option>
<mcq-option>(C) Decagon</mcq-option>
<mcq-correct>(D) Hexagon</mcq-correct>

Question 2

<mcq-correct>(A) Not Regular</mcq-correct>
<mcq-option>(B) Regular</mcq-option>
</answer>

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Answer:

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<reasoning>

Count the sides of the polygon

To classify the polygon, we first count the number of its sides (or vertices). Looking at the shape in the upper right corner, we can count:

1. Top horizontal-ish side
2. Upper-right slanted side
3. Lower-right slanted side
4. Bottom horizontal-ish side
5. Lower-left slanted side
6. Upper-left slanted side

There are exactly 6 sides.

Classify the polygon by its sides

A polygon with 6 sides is defined as a hexagon.

• A nonagon has 9 sides.
• A rectangle is a specific 4-sided quadrilateral.
• A decagon has 10 sides.
• A hexagon has 6 sides.

Therefore, the correct choice for part (a) is Hexagon.

Analyze if the polygon is regular

A regular polygon must be both equilateral (all sides are equal in length) and equiangular (all interior angles are equal).
Looking closely at the given hexagon:

• The top and bottom horizontal sides are noticeably shorter than the slanted side segments.
• The interior angles are not all equal.

Since the side lengths and interior angles are not all congruent, the polygon is Not Regular.
</reasoning>

<answer>

Question 1

<mcq-option>(A) Nonagon</mcq-option>
<mcq-option>(B) Rectangle</mcq-option>
<mcq-option>(C) Decagon</mcq-option>
<mcq-correct>(D) Hexagon</mcq-correct>

Question 2

<mcq-correct>(A) Not Regular</mcq-correct>
<mcq-option>(B) Regular</mcq-option>
</answer>

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