The Latest Regular Polygon Side Count Statistics Explained
A regular polygon with 3 sides is known as an equilateral triangle.
The statement “A regular polygon with 3 sides is known as an equilateral triangle” is a basic concept in geometry. A regular polygon is a polygon with all sides of equal length and all angles of equal measure. An equilateral triangle is a specific type of triangle where all three sides are equal in length and all three angles are equal to 60 degrees. Therefore, when a polygon has three sides that are all equal in length, it automatically satisfies the criteria to be classified as an equilateral triangle. This relationship highlights the fundamental connection between regular polygons and specific types of triangles in geometry.
A square, which is a regular polygon with 4 sides, has each internal angle equal to 90°.
The statistic states that a square, which is a regular polygon with 4 sides, has each internal angle equal to 90°. This means that when the four sides of a square meet at each corner, the angle formed at each corner is a right angle measuring 90 degrees. This unique property of squares is a characteristic of regular polygons, where all sides are of equal length and all angles are congruent. In the case of the square, the combination of straight sides and right-angle corners makes it a highly symmetrical and geometrically simple shape, often utilized in mathematics and design due to its precise and predictable properties.
A regular pentagon has 5 sides with interior angles of 108° each.
The given statistic states that a regular pentagon, which is a polygon with five equal sides, has interior angles of 108 degrees each. In a regular pentagon, all sides are of equal length, and all angles are of equal measure. Since the sum of the interior angles of any polygon can be calculated using the formula (n-2) 180 degrees, where n is the number of sides, for a pentagon with 5 sides, the total sum of interior angles is given by (5-2) 180 = 540 degrees. Therefore, each interior angle in a regular pentagon measures 108 degrees (540 degrees / 5 sides), making it a key property of this specific geometric shape.
Regular hexagons have 6 sides and each internal angle is 120°.
The statistic that regular hexagons have 6 sides and each internal angle is 120° refers to the geometric properties of a six-sided polygon where all sides are of equal length and all interior angles are congruent. In the case of a regular hexagon, each internal angle measures 120°, which is calculated by dividing the total sum of interior angles in any polygon (which is given by (n-2) 180, where n is the number of sides) by the number of angles. This property allows for regular hexagons to have a symmetrical and consistent shape, making them particularly useful in various design and mathematical applications.
An octagon is a regular polygon with 8 sides, and each internal angle is 135°.
The statistic states that an octagon is a regular polygon with eight equal sides and eight equal internal angles, each measuring 135 degrees. In other words, an octagon is a geometric shape with eight straight sides of the same length, and each of the eight interior angles is 135 degrees. Regular polygons are characterized by having all sides and angles equal in measure, making an octagon a symmetrical and balanced shape. Understanding the properties of an octagon, such as the equal-sided structure and the consistent internal angle measure of 135 degrees, is essential in geometric analysis and calculations.
Regular nonagon has 9 sides and each internal angle is 140°.
The statement that a regular nonagon has 9 sides and each internal angle is 140° describes a specific geometric property of a nonagon. A regular nonagon is a polygon with nine equal sides and nine equal internal angles. In this case, each internal angle of the regular nonagon is measured at 140°, meaning that when all nine angles are added together, the total sum equals 1260°. This information is important in geometry and mathematics, as it allows for the calculation of various properties and characteristics of the regular nonagon, such as its area, perimeter, and other geometric relationships.
The regular decagon has 10 sides and each internal angle has a measure of 144°.
The statistic states that a regular decagon, which is a polygon with 10 sides of equal length and 10 internal angles of equal measure, has each internal angle measuring 144 degrees. In a regular polygon, such as a decagon, all internal angles are congruent, which means they have the same measure. In this case, the measure of each internal angle in a regular decagon is 144 degrees. This information is useful in geometry and trigonometry for calculating various properties and relationships within the decagon, such as the exterior angles, diagonals, and area of the polygon.
Regular hendecagon is a polygon with 11 sides and interior angles of approximately 147.273°.
The statistic refers to the geometric properties of a regular hendecagon, which is a polygon with 11 sides of equal length and interior angles of approximately 147.273 degrees each. A regular polygon has congruent angles and sides, making the interior angles of a regular hendecagon equal to 147.273 degrees each. This information is important in geometry for understanding the properties and characteristics of polygons with different numbers of sides. By knowing the interior angles of a regular hendecagon, one can calculate various other properties, such as the exterior angles, the total sum of interior angles, and the symmetry of the shape.
A regular polygon with 12 sides is called a dodecagon and has interior angles of 150°.
The statistic states that a regular polygon with 12 sides, known as a dodecagon, will have interior angles measuring 150 degrees each. This means that regardless of the size of the dodecagon, each of its 12 angles will always be equal to 150 degrees. Regular polygons are geometric shapes with all sides and angles of equal length and measure, making them highly symmetrical. In the case of a dodecagon, the sum of all its interior angles will be 1800 degrees (12 angles 150 degrees), following the formula for calculating the sum of interior angles in any polygon: (n-2) 180, where n is the number of sides.
References
0. – https://www.www.mathbitsnotebook.com
1. – https://www.www.britannica.com
2. – https://www.www.mathopenref.com
