Square Perimeter Formula

          

        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

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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

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