Perimeter of polygons — regular and irregular

1.2.11 · Maths › Basic Geometry

Core Concept: Saari Sides Jodhna

Yeh definition kyun? Ek polygon ek closed figure hota hai jo straight line segments se bana hota hai. Uske around poora chakkar lagane ke liye, tum har side ko exactly ek baar traverse karte ho. Total distance bas un saari lengths ko jodne se milti hai.

Yeh universal kyun hai? Yeh definition kisi bhi polygon ke liye kaam karti hai — triangle, quadrilateral, pentagon, irregular shapes, sab ke liye. Sirf ek requirement hai: figure closed honi chahiye.

Figure — Perimeter of polygons — regular and irregular

Regular Polygons: Shortcut Wala Tarika

Regular polygons ke liye perimeter formula derive karna:

Step 1: General perimeter formula se shuru karo: $P = s_{1} + s_{2} + s_{3} + \dots + s_{n}$

Step 2: Regular polygon mein har side ki length same hoti hai. Iss length ko $s$ bolte hain: $s_{1} = s_{2} = s_{3} = \dots = s_{n} = s$

Step 3: Sum mein substitute karo: $P = s + s + \dots + s (n times)$

Step 4: Same number ko $n$ baar jodna multiplication hai: $P = n \times s$

Irregular Polygons: Koi Shortcut Nahi

Irregular polygons ke liye (alag alag lengths wali sides), koi multiplication shortcut nahi hai. Tumhe har side alag alag measure karke jodni padegi.

Regular formula kyun use nahi kar sakte? Formula $P = n \cdot s$ assume karta hai ki saari sides equal hain. Agar nahi hain, toh tum kisi average ya arbitrary cheez se multiply kar rahe hoge — jo actual perimeter nahi deta.

Common Mistakes Aur Unhe Kaise Theek Karein

Deep Samajh: Alag Alag Polygons Mein Same Principle Kyun?

First principles se:

Distance kya hai? Yeh measure karta hai ki do points kitne door hain ek dusre se.
Polygon kya hai? Connected line segments ki ek sequence jo ek closed loop banati hai.
Perimeter kya hai? Boundary ke around travel ki gayi total distance.

Kyunki har side ek straight segment hai, uski length bas uske endpoints ke beech ki distance hai. Total distance pane ke liye, hum in saari individual distances ko jodte hain — yahi perimeter hai.

Regular vs. Irregular: Difference perimeter ki definition mein nahi hai (hamesha sides ka sum), balki yeh hai ki kya hum arithmetic simplify kar sakte hain. Regular polygons hume factor karne dete hain: $s + s + s + s = 4 s$ . Irregular polygons nahi dete.

Units Aur Real-World Applications

Units: Perimeter length ke units mein measure hota hai:

Metric: mm, cm, m, km
Imperial: inches, feet, yards, miles

Units ki parwah kyun karein? Agar side lengths cm mein hain, toh perimeter cm mein hoga. Agar ek side meters mein hai aur doosri centimeters mein, pehle convert karo!

Real applications:

Fencing: Ek field band karne ke liye kitni wire chahiye?
Framing: Picture ya door frame karne ke liye kitni wood chahiye?
Track length: Running track ka perimeter (aksar rectangular hota hai semicircular ends ke saath)
Borders: Room ya garden bed ke around decorative trim

Connections

Area of polygons — perimeter boundary measure karta hai, area interior measure karta hai
Triangles — sabse simple polygon, $P = a + b + c$ ya $P = 3 s$ agar equilateral ho
Quadrilaterals — rectangles, squares, trapezoids sab ka perimeter = 4 sides ka sum
Circles — circle ka perimeter circumference kehlata hai, sides ki jagah $π$ use hota hai
Pythagorean theorem — perimeter calculate karne se pehle right triangles mein side lengths dhundne ke liye often zaroori hota hai
Units of measurement — jodhne se pehle hamesha units check aur convert karo

Recall Ek 12-saal ke bacche ko samjhao

Socho tum chalk se zameen par ek shape bana rahe ho. Tum ek corner se shuru hote ho aur har edge ke saath chalte ho, mark karte hue, jab tak wapas wahi nahi aa jaate jahan se shuru kiya tha. Jitni total distance chale, wahi perimeter hai.

Agar tumhari shape ek square hai aur har side 5 kadam lambi hai, tum 5 kadam chaar baar chalte ho: $5 + 5 + 5 + 5 = 20$ kadam. Yeh kehna zyada aasaan hai $4 \times 5 = 20$ . Yeh ek regular shape hai — saari sides same.

Lekin agar tumhari shape weird hai, jaise ek pahadi garden jis ki sides 3 kadam, 7 kadam, 4 kadam, aur 5 kadam hain, tum bas multiply nahi kar sakte. Tumhe unhe ek ek karke jodna hoga: $3 + 7 + 4 + 5 = 19$ kadam. Yeh ek irregular shape hai.

Perimeter bas "kitna around?" hai — hamesha saare edges jodo.

#flashcards/maths

Polygon ka perimeter kya hota hai? :: Uski saari sides ki lengths ka sum.

Regular polygon kya hota hai?

Ek aisa polygon jismein saari sides ki length equal hoti hai aur saare interior angles equal hote hain.

n

sides wale regular polygon ka perimeter formula jahan har side

s

ho?

P = n \cdot s

Irregular polygons ke liye

P = n \cdot s

use kyun nahi kar sakte?

Kyunki sides ki alag alag lengths hoti hain; yeh formula assume karta hai ki saari sides equal hain.

8 cm side wale equilateral triangle ka perimeter?

P = 3 \times 8 = 24

Ek quadrilateral ki sides 3 cm, 5 cm, 7 cm, aur 4 cm hain. Uska perimeter kya hai?

P = 3 + 5 + 7 + 4 = 19

Perimeter kis unit mein measure hota hai?

Length ke units mein (cm, m, inches, feet, etc.) — area ki tarah squared units mein nahi.

Ek regular hexagon ka perimeter 48 m hai. Har side ki length kya hai?

s = P / n = 48/6 = 8

Sach ya Jhooth: Perimeter aur area ek hi cheez measure karte hain.

Jhooth. Perimeter boundary measure karta hai (length), area interior surface measure karta hai.

Regular vs irregular polygons ka perimeter dhundne mein kya key difference hai?

Regular: sides ki sankhya ko ek side length se multiply karo. Irregular: har alag side length alag alag jodo.