Perimeter and Area Part 6.1 | Maths | #mathclass6 #kvs #nvs #ganitaprakash #ncertclass6 #cbseclass6

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[cbsewithsudhir]

CBSE WITH SUDHIR

PERIMETER AND AREA : Sudhir Sir's personal notes

MATHS CLASS 6

Perimeter of a rectangle = 2 x (length + breadth)

Perimeter of a square = 4 x length of a side

Perimeter of a triangle = Total sum of lengths of its three sides

What happens when you shift from left to right side and vice versa in an Equation

In algebra, moving terms across the equals sign in an equation involves maintaining the balance of both sides. The key rule is inverse operations : When you move a term from one side of the equation to the other, you must apply the opposite (or inverse) operation.

- Addition ↔ Subtraction
- Multiplication ↔ Division

If a term is added, subtract it on both sides.

Example: x + 2 = 5
Move the +2 term by subtracting 2 from both sides.
x = 5 - 2
x = 3

If a term is subtracted, add it on both sides.

Example: x - 7 = 3
Move the -7 by adding 7 to both sides.
x = 3 + 7
x = 10

If a term is multiplied, divide it on both sides.

Example: 2x = 10
Move the 2 by dividing both sides by 2.
x = 10 divided by 2
x = 5

If a term is divided, multiply it on both sides.

Example: x divided by 4 = 8
Move the 4 by multiplying both sides by 4.
x = 8 x 4
x = 32

Figure it out questions

1. (a) Perimeter of a rectangle = 2 x (l + b)

Perimeter = 14 cm
Breadth = 2 cm

So 14 = 2 x (l + 2)

14 = 2l + 4
2l = 14 - 4
2l = 10
l = 10/2 = 5 cm

(b) Perimeter of a square = 4 x side of square (s)

20 = 4 x s
s = 20/4 = 5 cm

(c) Perimeter of a rectangle = 2 (l + b)

12 m = 2 (3 + b)
12 = 6 + 2b
12 - 6 = 2b
6 = 2b
6/2 = b
So b = 3 m

This means this rectangle is actually a square.

2. Perimeter of Rectangle = 2 (5 + 3) = 2 (8) = 16 cm

Now when the wire is straightened, its length and then the perimeter of the Square it will form is 16 cm.

So perimeter of square = 16 cm
4s = 16 cm
s = 16/4 = 4 cm

3. Perimeter of triangle = 55 cm
First side of triangle = 20
Second side of triangle = 14 cm

Perimeter of a triangle = Total sum of lengths of its three sides

So 55 = 20 + 14 + a
55 = 34 + a
55 - 34 = a
so a = 21 cm

Therefore length of third side of triangle is 21 cm.

4. To find the cost of fencing, we need to first calculate the perimeter of the rectangular park.

Length = 150 m
Breadth = 120 m

Perimeter = 2 (l + b)
Perimeter = 2 (150 + 120)
Perimeter = 2 (270)
Perimeter = 540 m

Now fence costs Rs 40 per metre so 540 m x 40 / metre = Rs 21600

5. (a) 36 = 4a
so a = 36/4 = 9 cm

(b) 36 = 3a
so a = 36/3 = 12 cm

(c) 36 = 6a
so a = 36/6 = 6 cm

6. Perimeter of rectangular field = 2 (l + b)
Here, l = 230 m and b = 160 m

So p = 2 (230 + 160)
p = 2 x 390
p = 780 m

He needs three rounds of rope so 3 x 780 = 2340 m of rope is needed.

Matha Pachchi

Let us mark the four corners of the outer track as MNOP

Let us mark the four corners of the inner track as EFGH

So perimeter of rectangular track MNOP = 2 (l + b)

2 x (70 + 40) = 2 x (110) = 220 m

Perimeter of rectangular track EFGH = 2 x (60 + 30) = 2 x (90) = 180 m

Figure it out

1. Distance covered by Akshi (running on the outer track MNOP) in 5 rounds is = 5 x perimeter of MNOP = 5 x 220 = 1100 m

2. Distance covered by Toshi (running on the inner track ABCD) in 7 rounds = 7 x perimeter of EFGH = 7 x 180 = 1260 m

Toshi ran the longer distance.

3. (a) Akshi's total distance is 220 m but we have to mark `A' at the point where Akshi will be after she ran 250 m.

So this will mean she has completed one round and then has run an extra 30 m (250 - 220). So we have to mark `A' 30 m from the starting point M along the length.

(b) Distance per round is 440 pm (220 x 2). So 500 will mean she will 60 m from the starting point after completing two rounds. So `B' will be marked along the length.

(c) To find out how many full rounds, we will divide 1000/220 = 4.545. This means she has completed 4 full rounds but not completed the fifth round.

To find out the remaining distance, 1000 m - (4 x 220 m) = 1000 - 880 = 120 m.

This will be 70 + 40 + 10 so Akshi will be on the upper side of the park 10 m from position `O'.

(d) Perimeter of the inner track = 180 m

So if Toshi has run 250 m, it means she has run 250 - 180 = 70 m on the second round.

One side length is 60 m so it means the position X will be 10 m after point F.

(e) 180 x 2 = 360 m

500 - 360 = 140 m so this is the distance Toshi has run on the third round. So 140 m will mean 10 m short of point H.

(f) Toshi ran 1000 m so 1000/ 180 = 5.56 so she has finished 5 full rounds but not completed the 6th round.

Remaining distance = 1000 - (5 x 180) = 1000 - 900 = 100 m.

So position Z will be 10 m after position G.

DEEP DIVE

First runner will start his race from 50 metres before common finish line. (400 - 350 = 50 m)

Second runner will start 250 m before common finish line. (600 - 350 = 250 m)

Perimeter of a Regular Polygon

Estimate and Verify

Figure One : 8s + 2d

Figure Two : 4s + 6d

Figure Three : 12s + 6d

Figure Four : 18s + 6d

Perimeter of a Regular Polygon

The similarity is that all three and four sides will be equal.

Other objects - Ruler, Front cover of your Ganita Prakash Textbook

Split and Rejoin

(b) One side is 6 cm. But it is added to 2 cm which makes it 8 cm.

So it will be 6 cm + 2 cm + 6 cm + 2 cm + 4 cm + 6 cm + 2 cm = 28 cm

(c) Total boundary (from Bottom base) = 6 cm + 2 cm + 2 cm + 6 cm + 2 cm + 6 cm + 2 cm + 2 cm = 28 cm

(d) Total length of boundary from left pillar = 6 cm + 2 cm + 2 cm + 3 cm + 3 cm + 2 cm + 2 cm + 6 cm = 26 cm

[Drawwithme]

Hello sir first calculation is wrong u have said 1000;1000;900;900 steps so it should be 3800 steps which then should be multiplied by 10 that is 38000 steps
Thank you for the clear and to the point explanation

[mouliomk]

Very interesting and easy to understand sir

[rayihanrazakhan]

sir jo figur it out ka 1 q . 2q. hai vo smaj mai aaya

[arbindkumarsingh]

Sir what's the meaning of bandhu 🤔🤔

[gameryash]

Good evening sir, but in my class ma'am has not gone in sequence she was going ulernate chapters