Class 6 ยท Maths ยท Ganita Prakash
Chapter 6 ๐
Chapter 6 ๐
Perimeter and Area
Quick, colourful revision notes โ easy to read before your test!
Chapter Contents
6.1 Perimeter
Perimeter โ the total distance covered along the boundary of a closed shape, once all the way around. For a polygon, it's just the sum of all its side lengths.
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Fig 1: Perimeter formulas for rectangle, square and triangle
| Shape | Perimeter Formula |
|---|---|
| Rectangle | 2 ร (length + breadth) |
| Square | 4 ร side |
| Triangle | sum of all 3 sides |
6.2 Area
Area โ the amount of surface (region) enclosed by a closed shape, measured in square units (sq m, sq cm...).
| Shape | Area Formula |
|---|---|
| Rectangle | length ร breadth |
| Square | side ร side |
A 5 m ร 4 m floor (area 20 sq m) with a 3 m ร 3 m carpet (area 9 sq m) leaves 20 โ 9 = 11 sq m uncarpeted.
To estimate area on a squared grid: count a full square as 1, count more-than-half a square as 1, ignore less-than-half, and count an exact half as ยฝ. Squares are used (not circles) because they tile perfectly with no gaps.
6.3 Area of a Triangle
Cut a rectangle along its diagonal โ you get two triangles.
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Fig 2: A rectangle's diagonal always splits it into two equal-area triangles
Area of a triangle = ยฝ ร Area of the rectangle built around it (same base and height). This works even for triangles that don't look like "half a rectangle" at first glance!
Same Area, Different Perimeter
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Fig 3: 9 unit squares arranged as a compact block vs. a long strip
Shapes with the same area can have very different perimeters! A more "spread out" shape (like a thin strip) has a bigger perimeter than a "compact" shape (like a square) for the same area.
๐ฏ Quick Summary
- Perimeter = total boundary length; Rectangle: 2ร(l+b), Square: 4รside, Triangle: sum of sides.
- Area = surface enclosed, in square units; Rectangle: lรb, Square: sideรside.
- On grid paper: count full/more-than-half squares as 1, ignore less-than-half, half squares as ยฝ.
- Area of a triangle = ยฝ ร Area of the surrounding rectangle.
- Same area can give very different perimeters โ compact shapes have smaller perimeters than spread-out ones.
โ๏ธ Notes by @edugrown โ happy revising! ๐