# Square Perimeter Formula:-

### Today in this article, I will explain on the topic perimeter of square.To start writing on perimeter of square I want to explain you ,

## ***What is perimeter of a shape?

### Answer:- In one word, perimeter means the total length of whole fence of a closed shape or a open shaped body either it may be two dimensional (triangle,rectangle etc) or three dimensional (cuboid,cube etc.)

## ***What is the perimeter of a square?

### Answer:- We know that perimeter of a quadrilateral is the sum of its all four sides,so square is also a quadrilateral. Therefore, its perimeter will also be the sum of its all four sides,but all sides of a square are equal,so perimeter of a square will be,

### = 4× side

## ∴ Square perimeter formula

= a+a+a+a= 4×a, where a= length of each side of a square.

## **Problems related on the perimeter of a square:-

## ***1)Each side of a square garden is 15m, then find its perimeter.

### Answer:- Here,

### Each side of the square garden(a)= 15m

∴ Perimeter of the garden = 4×a

= (4×15)m

= 60 m

## ***2) The perimeter of a square field is 40cm

Find its each side.

### Answer:-∵ The perimeter of the field=40cm

### Let,

### each side of the field = a

### ∴ each side of the field (a)= 40/4

=10 cm

Area of a square:-

If each side of a square =a unit

Then,

area of the square = a² square unit

i.e; area of the square = side× side

## ***Prove that area of square = a², where a= Each side of the square.

### Answer:- ∵ Let, ABCD is a square,

∵ All sides of a square is equal,

Let , each side of the square = a unit

Construction:- Diagonal AC is joined

### Proof:- ∵ Diagonal of a square divides it into two equal ares of triangles,

### So AC divides ABCD into two equal areas of triangles i.e;

ar(ABC) = ar(ADC)

Now ar(ABC) = ½ AB× BC

= ½ a×a sq.unit [∵ABCD is a square.∴ <B=90°, as angles of a square are equal measures 90°]

= ½ a² sq.unit…….(i)

###

similarly,

ar(ADC) = ½ CD× AD

= ½ a×a sq.unit [<D=90°]

= ½ a² sq unit …..(ii)

Noe,

area of square ABCD = ar(ABC)+ar(ADC)

=½ a² +½ a²

= a² square unit,

Proved

## ***Problems related on square area formula:-

## ***(1) Each side of a square is 10cm, find its area.

### Answer:- Each side of a square(a) = 10cm

∴ Area of the square = a²

=10² cm²

= 10×10 cm²

= 100cm²

## ***(2)Area of a square plot is 400m², Find its each side.

### Answer:- ∵ Area of the square plot =400m²

## FREQUENTLY ASKED QUESTIONS:-
##
What is the perimeter of a triangle?

Answer:- The perimeter of a triangle is sum of its all three sides.Mathematically, perimeter of a triangle = a+b+c, where a=measure of 1st side of the triangle,b=measure of 2nd side of the triangle and c=measure of 3rd side of the triangle

## what is half or semi perimeter of a triangle?

Answer:- Half or semi perimeter of a triangle =1/2(a+b+c), where, a,b and c are three different sides of the triangle.

## what is the perimeter of an equilateral triangle?

Answer:- The perimeter of an equilateral triangle = a+b+c, where a,b and c are the sides of equilateral triangle,∵ equilateral has all sides equal,so its actual perimeter=3×a, where a = measure of each side of equilateral triangle.

## What is the perimeter of a square?

Answer:- The perimeter of a square = 4 × a where , a = length of each side of the square.

##
what is the perimeter of rhombus?

Answer:- The perimeter of rhombus = 4 × a where, a = length of each side of the rhombus as all sides of the rhombus are equal.

## What is the perimeter of a parallelogram?

.
Answer:- The perimeter of a parallelogram = 2 (l+b) where, l = length of the of the parallelogram and b = breadth of the parallelogram

## What is the perimeter of a triangle?

Answer:- The perimeter of a triangle is sum of its all three sides.Mathematically, perimeter of a triangle = a+b+c, where a=measure of 1st side of the triangle,b=measure of 2nd side of the triangle and c=measure of 3rd side of the triangle

## what is half or semi perimeter of a triangle?

Answer:- Half or semi perimeter of a triangle =1/2(a+b+c), where, a,b and c are three different sides of the triangle.

## what is the perimeter of an equilateral triangle?

Answer:- The perimeter of an equilateral triangle = a+b+c, where a,b and c are the sides of equilateral triangle,∵ equilateral has all sides equal,so its actual perimeter=3×a, where a = measure of each side of equilateral triangle.

## What is the perimeter of a square?

Answer:- The perimeter of a square = 4 × a where , a = length of each side of the square.

## what is the perimeter of rhombus?

Answer:- The perimeter of rhombus = 4 × a where, a = length of each side of the rhombus as all sides of the rhombus are equal.

## What is the perimeter of a parallelogram?

. Answer:- The perimeter of a parallelogram = 2 (l+b) where, l = length of the of the parallelogram and b = breadth of the parallelogram

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