Formula for the perimeter of a rectangle and square. Examples, Solution on perimeter of a rectangle and square.

__UNIT−1__

__GEOMETRY__

** **

__Perimeter and Area__

__Perimeter of the rectangle and square__

** **

**Situation**

Raju is a class 5 student of a
Panchayat union middle school. Raju's head master wanted to fence the school as
there is disturbance caused by the tresspassers. Hence the headmaster decided
to fence the school.

The headmaster asked Raju and his
classmates to measure the length of the boundary of the school premises, so as
to buy the required fencing wire.

Raju and his friends measured the
length of each side and added them to find the total length.

Length of the boundary = sum of the
length of each side

Here the length of the boundary is
called as perimeter,

Hence, the sum of the length of all
the sides of a closed area is called its perimeter

Perimeter is used in framing a photo,
for fencing a vacant land, etc..,

**Activity 1**

**Write the perimeter of each figure:**

1.

Perimeter of rectangle

P = (2×1) + (2×b)

= (2×6) + (2×5)

= 12 + 10

P = 22cm

2.

Perimeter of square

P = 4 × a

= 4×4

P = 16cm

3.

Perimeter of triangle

P= a+b+c

= 3+7+5

P = 15cm

4.

Perimeter

P = 9+6+3+4+3+4+3+6

P= 38 cm

5.

Perimeter

P = 10+5+5+10+5+5

P = 40 cm

6.

Perimeter

P = 11+16+7+7+16

P = 57 cm

** **

__Formula for the perimeter of a rectangle:__

Perimeter
= length + breadth + length + breadth (opposite sides of a rectangle are equal)

So,
the perimeter of a rectangle = twice the length + twice the breadth

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

__Example
1.1__

The
length of the rectangle below is 5cm and its breadth is 2cm. Find its perimeter.

**Solution**

Perimeter
of rectangle PQRS = (2 × length) + (2 × breadth)

=
(2 × 5) + (2 × 2)

=
10+4

=
14

Therefore,
the perimeter of the rectangle is 14 cm.

__Formula for the perimeter of a square__

The
lengths of all the sides of a square are equal.

Therefore,
the perimeter of a square = four time the length of one of its sides

Perimeter
of a square = 4 × (the length of one side)

** **

__Example
1.2__

The
length of one side of a square is 7cm. Find its perimeter.

**Solution**

The
perimeter of a square is four times the length of one side.

Perimeter
of a square = 4 × (length of one side)

=
4 × 7

=
28

Therefore,
the perimeter of the square is 28 cm

** **

__Example
1.3__

The
length of a rectangular park is 60 cm, while its width is 50 cm. What is its
perimeter?

**Solution**

Perimeter
of the rectangle = (2 × length) + (2 × breadth)

=
(2 × 60) + (2 × 50)

=
120 + 100

=
220

Therefore, the perimeter of the
rectangular park is 220 cm.

** **

__Example
1.4__

How
much wire will be needed to put a triple fence around a square plot with side
20m? What will be the total cost of the wire at ₹ 50 per metre?

**Solution**

To
put a single fence around the square plot, we need to find its perimeter

Perimeter
of a square = 4 × length of one side = 4 × 20 = 80

The
perimeter of the square plot is 80 metres. Since the fence is to be a triple
fence we must triple the perimeter

80
× 3 = 240 m of wire will be needed to fence the square plot.

Now
let us find out how much the wire will cost. One metre of wire costs ₹ 50

Therefore
the cost of 240 m of wire will be 240 × 50 = 12,000

The
total cost of wire for putting a triple fence around the plot will be ₹ 12,000

**Try this**

If a square of side 1 cm is cut out of the corner of a larger
square with side 4 cm (See the figure). What will be the perimeter of the
remaining shape?

Perimeter of square P = 4 × a

= 4×4

= 16cm

Perimeter of cut out square P = 4 × a

= 4 × 1

= 4cm

Perimeter of the remaining shape = 16−4

= 12 cm

Tags : Geometry | Term 3 Chapter 1 | 5th Maths , 5th Maths : Term 3 Unit 1 : Geometry

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

5th Maths : Term 3 Unit 1 : Geometry : Perimeter of the rectangle and square | Geometry | Term 3 Chapter 1 | 5th Maths

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