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Class IV - Maths: Borders and boundaries
One Word Answer Questions:
Q) Write the name of below image
    
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Short Answer Questions:
Q) What is the area of triangle?
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Q) What is the perimeter of a square?
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Q) What is the perimeter of a rectangle?
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Q) How many sides in a square?
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Q) Find the perimeter of a rectangle whose length is 7 cm and breadth is 2.5 cm?
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Q) Find the side of a square whose perimeter is 32cm?
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Q) Find the perimeter of a square whose side is 2cm?
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Q) Find the perimeter of a triangle whose sides are 10 cm, 15 cm, and 5cm
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Q) Find the perimeter of a rectangle whose length is 9 cm and breadth is 5 cm.?
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Long Answer Questions:
Q) Find the perimeter of square with side 12 m?
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Q) Find the perimeter of rectangle with length 3cm and breadth 8 cm?
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Q) Mrs Nehra bought a carpet measuring 8.5 m by 7 m. What is the perimeter of the carpet?
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Q) Find the side of a square whose perimeter is 36cm?
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Q) Find the perimeter of a lawn of length 25 m and breadth 15 m?
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    Borders
    PERIMETER

    Definition

    "The perimeter of a figure is the total distance around the edge of the figure".

    Factors and Multiples

    Examples:

    1. Find the perimeter

    Factors and Multiples

    1. Find the perimeter of star

    Factors and Multiples

    1. Find the perimeter

    Factors and Multiples
    Solution

    Perimeter= 5 + 5 + 14+ 8 + 2 = 34m

Perimeter By Using A Formula

The perimeter of some polygons can be calculated directly by using a formula.
Let us calculate the perimeter of a rectangle and square by using a formula.

PERIMETER OF A RECTANGLE

In a rectangle, the perimeter is the sum of all its sides.

Factors and Multiples
Therefore, perimeter        = l + b + l + b
                                 = l + l + b + b
                                 = 2× l + 2 × b
                                 = 2 (l + b)
Perimeter of a rectangle = 2 ( length + breadth )

Examples:

1. Find the perimeter of a rectangle whose length is 5 cm and breadth is 4 cm.
Solution:

Factors and Multiples

Here, length of the rectangle = 8 cm
Breadth of the rectangle = 5 cm
Perimeter of the rectangle = 2 (length + breadth)
= 2 (8 cm + 5 cm)
= 2 (13 cm)
= 26 cm.
Hence, the perimeter of the rectangle is 26 cm.

2. Find the length of the wire required to fence 3 rounds of a rectangular ground of length 20 m and breadth 15 m. Also find the cost of fencing the ground at the rate of ₨ 2 per metre.
Solution: Length of the ground = 20 m
Breadth of the ground = 15 m
Perimeter = 2 (length + Breadth)
= 2 (20 + 15)
= 2(35)
= 70m
Total wire required to fence 3 rounds of ground
= 3 × 70 m = 210 m
Cost of fencing 1m = ₨ 2
Cost of fencing 210 m = 210 × 2
Cost of fencing = ₨ 420

PERIMETER OF A SQUARE

"The sum of all the sides of a square is its perimeter".

Factors and Multiples

Therefore, Perimeter of a square = 4s = 4 × side
Examples:
1. Find the perimeter of a square whose side is 13 cm.
Solution:

Factors and Multiples

Side of a square = 13 cm
Perimeter of a square = 4 × side
= 4 × 13 cm
= 52 cm.

2. Find the side of a square whose perimeter is 36 cm.
Solution: Perimeter of the square = 36 cm
Perimeter = 4 × side
36 = 4 × side
Side = 36 ÷ 4
Side = 9 cm.

PERIMETER OF A TRIANGLE

"The sum of measure of three sides of a triangle is its perimeter".

Factors and Multiples

So, Perimeter of a triangle, P = a + b + c
Example: Find the perimeter of a triangle whose sides are 11 cm, 13 cm, and 8 cm
Solution:

Factors and Multiples

Perimeter of a triangle = sum of its sides
= 11 + 13 + 8
= 32 cm
So, the perimeter of the triangle = 32 cm.

Boundaries

"The perimeter of a circle is the distance around the outside".

Factors and Multiples

Circumference of a circle

Find the circumference of the circle for radius 4

Factors and Multiples

Radius = 4
circumference of circle (c)= 2Πr
circumference of circle (c)= 2 × 3.14r
circumference of circle (c)= 6.28r
circumference of circle (c)= 6.28×4
circumference of circle (c)= 25.12

Examples

1. Find the circumference of the circle for radius 5

Factors and Multiples

2.Find the circumference of the circle for radius 3

Factors and Multiples

Radius = 3
circumference of circle (c)= 2Πr
circumference of circle (c)= 2 × 3.14r
circumference of circle (c)= 6.28r
circumference of circle (c)= 6.28×3
circumference of circle (c)= 18.84

3.Find the circumference of the circle for radius 2.5

Factors and Multiples

Radius = 2.5
circumference of circle (c)= 2Πr
circumference of circle (c)= 2 × 3.14r
circumference of circle (c)= 6.28r
circumference of circle (c)= 6.28×2.5
circumference of circle (c)= 15.7

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