Regular Polygons (नियमित बहुभुज) In Hindi
1. बहुभुज एक समतल, द्वि-आयामी आकृति होती है जिसकी भुजाएँ सीधी होती हैं। 2. समबहुभुज एक विशेष प्रकार का बहुभुज होता है जिसकी सभी भुजाएँ लंबाई में बराबर होती हैं और सभी आंतरिक कोण माप में समान होते हैं।Regular Polygons In English
1. A polygon is a flat, two-dimensional shape with straight sides. 2. A regular polygon is a special type of polygon where all sides are equal in length and all interior angles are equal in measure. 3. Example: A square is a polygon with made by joining 4 straight lines of equal length.Parts of a Polygon A polygon has three parts:Sides: A line segment that joins two vertices is known as a side. Vertices: The point at which two sides meet is known as a vertex. Angles: interior and exterior. An interior angle is the angle formed within the enclosed surface of the polygon by joining the sides.Properties of Regular PolygonsThe properties of regular polygons are listed below:1. All its sides are equal. 2. All its interior angles are equal. 3. The sum of its exterior angles is 360°.Equilateral TriangleAn equilateral triangle is a specific type of regular polygon with three equal sides and three equal angles. It’s one of the most fundamental shapes in geometry.Properties of an Equilateral Triangle:1. All three sides are congruent (equal in length). 2. All three angles are congruent (equal in measure) and each angle measures 60 degrees. 3. The sum of all interior angles is 180 degrees (as with any triangle). 3. Every equilateral triangle has three lines of symmetry.Equilateral Triangle formulaPerimeter: The perimeter P of an equilateral triangle with side length s is given by:- P = 3s
- A = \( \frac{√3}{4} \) x \( s^2 \)
- h = \( \frac{√3}{2} \) x s
- R = \( \frac{s}{√3} \)
- P = 4s
- A = \( s^2 \)
- r = \( \frac{s}{2} \)
- P = 5s
- A = \( \frac{1}{2} \) x a x P
- a = \( \frac{s}{2tan(π/5)} \)
- P = 6s
- A = \( \frac{3√3}{2} \) x \( s^2 \)
- a = \( \frac{s}{2} \) x √3
- P = 7s
- A = \( \frac{7}{4} \) x \( s^2 \) x cot (\( \frac{π}{7} \))
- P = 8s
- A = 2(1 + √2) x \( s^2 \)
- a = \( \frac{s}{2} \) x √2(1+√2)
- P = 9s
- A = \( \frac{9}{4} \) x \( s^2 \) x cot (\( \frac{π}{9} \))
- a = \( \frac{s}{2} \) x cot (\( \frac{π}{9} \))
- P = 10s
- A = \( \frac{5}{2} \) x \( s^2 \) x tan (\( \frac{π}{10} \))
- a = \( \frac{s}{2} \) x tan (\( \frac{π}{10} \))
- P = 11s
- A = \( \frac{s}{2} \) x \( s^2 \) x cot (\( \frac{π}{11} \))
- a = \( \frac{s}{2} \) x cot (\( \frac{π}{11} \))
- P = 12s
- A = \( 3s^2 \) x cot (\( \frac{π}{12} \))
- A = \( \frac{s}{2} \) x cot (\( \frac{π}{12} \))
Leave a Reply