Podcast
Questions and Answers
What is the sum of the interior angles of a polygon with 10 sides?
What is the sum of the interior angles of a polygon with 10 sides?
- 1080 degrees
- 900 degrees
- 720 degrees
- 1440 degrees (correct)
Which type of polygon has all sides of equal length and all angles of equal measure?
Which type of polygon has all sides of equal length and all angles of equal measure?
- Irregular polygon
- Scalene polygon
- Convex polygon
- Regular polygon (correct)
What characteristic defines a concave polygon?
What characteristic defines a concave polygon?
- All sides are of different lengths.
- It has at least one interior angle greater than 180 degrees. (correct)
- All vertices point outward.
- All angles are less than 180 degrees.
Which of the following formulas is used to calculate the area of a regular polygon?
Which of the following formulas is used to calculate the area of a regular polygon?
What is the minimum number of sides a polygon must have?
What is the minimum number of sides a polygon must have?
Flashcards
Sum of interior angles of a 10-sided polygon?
Sum of interior angles of a 10-sided polygon?
1440 degrees
What is a regular polygon?
What is a regular polygon?
A polygon with all sides and all angles equal.
What defines a concave polygon?
What defines a concave polygon?
A polygon with at least one interior angle > 180 degrees.
Formula to calc. area of a regular polygon?
Formula to calc. area of a regular polygon?
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Minimum number of sides a polygon must have?
Minimum number of sides a polygon must have?
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Study Notes
Interior Angles of a Polygon
- The sum of the interior angles of a polygon can be calculated using the formula: (n - 2) × 180°, where n is the number of sides.
- For a polygon with 10 sides, the sum is (10 - 2) × 180° = 8 × 180° = 1440°.
Regular Polygon Characteristics
- A regular polygon has all sides of equal length and all angles of equal measure, making it both equilateral and equiangular.
Concave Polygon Definition
- A concave polygon is defined by at least one interior angle that measures greater than 180°. This feature causes the shape to "cave in" towards the interior.
Area Calculation for Regular Polygons
- The area of a regular polygon can be calculated using various formulas, commonly: Area = (1/2) × Perimeter × Apothem or Area = (n × s^2) / (4 × tan(π/n)), where s is the length of a side.
Minimum Polygon Sides
- A polygon must have a minimum of three sides to be classified as such; shapes with fewer than three sides do not enclose a space.
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