Rectangle In Geometry | Properties of Rectangle| Formula and Shape of Rectangle

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Rectangle In Geometry | Properties of Rectangle| Formula and Shape of Rectangle

 

 

 1.Rectangle

 2.properties of Rectangle

3.Formula of Rectangle

4.Shape of Rectangle

 

   

Rectangle In Geometry

A quadrilateral (of four sides) with four right angles and out of four sides, opposite sides are equal and parallel .  The line joining two opposite non-adjacent corners of a quadrilateral  is called diagonal .The diagonals of  a Rectangle are equal  and bisect each other.

   

Rectangle In Geometry | Properties of Rectangle| Formula and Shape of Rectangle
Rectangle In Geometry | Properties of Rectangle| Formula and Shape of Rectangle


Properties of Rectangle

      some major properties of Rectangle  are listed below.
  
  • Rectangle consists of four sides .out of four sides opposite sides are equal and parallel.
  • all angles are right angle  .
  • diagonals are in same length.
  • diagonals bisect each other.
  • A diagonal  divides the rectangle into two equal triangles.   

likewise two diagonals creates four triangles after bisection in rectangle and opposite triangles formed by bisection are equal  .                                                                                                                                                                                                                                                                                                                                                                                                                                  

Formula of Rectangle

 Formula of Rectangle are listed below.

                       1.Area

                           2.Perimeter

       Area

      First of all we should understand :what is area?

        area is nothing but the the enclosure part or surface surrounded by the four sides of rectangle.
         
         if ABCD is a rectangle AB,BC,CD and DA are four sides of it.
       then area of a rectangle is the enclosure part of ABCD rectangle.
        for this we have to multiply the two sides of a ABCD.
         Area of a Rectangle = length*breadth.
         Length = Area/Breadth.
         Breadth = Area/Length.

    Perimeter

     Before remembering the formula for perimeter we should go through what does it mean
       perimeter. According to its meaning it is the continuous line forming the boundary of a closed           geometrical figure.
       if ABCD is a rectangle then its lines are  AB,BC,CD,DA.
       so its perimeter is the AB+BC+CD+AD
                  we know AB=CD and BC =DA  .    (consider the above fig)
               perimeter:=2(AB + BC)
                                =2(l + w)
       Perimeter of Rectangle = sum of all sides = 2(length + breadth).

    Some Examples on Rectangle

    1. Find the area and perimeter of the Rectangle whose sides are 10 cm and 8 cm respectively.
    Answer: –
        Area of the Rectangle=length*breadth.
        here mentioned length=10 cm
        and breadth = 8 cm
        so, area=10*8=80  cm²
     Perimeter of the Rectangle is = 2(length + breadth).
       Perimeter = 2(10+8) cm=36 cm.
    2. Find the Area of  a Rectangle whose diagonal is 5 cm and one of its side is 3 cm.
       
    Answer : –
        Area of the Rectangle=length*breadth.
    Here diagonal and। One side is giving.
    Applying Pythagoras rule we can find another side of the rectangle.
    Another side=   √(5² -3²)=4cm
    So Area=3*4= 12cm² .
     3. The Length and breadth of a rectangular  field  are in the ratio 5:3 .if the cost of cultivating the field  at 25 paisa per square  meter is Rs.6000,find the dimensions of the field.
     
    Answer:-– 25 paisa per square meter.

     

      6000.00 paisa is the cost of cultivating of square meter = 600000/25= 24000square meter.

     

    24000 square meter is the Area of the Rectangle.

     

    Now, we consider Length and Breadth of the rectangle are 5x and 3x.

     

    Area of theRectangle=length*breadth.

     

    5x*3x= 15x²

     

    15x² = 24000

     

    X² = 24000/15 = 1600

     

    x= √1600=40 meter.

     

    So, length = 5*40=200 meter

     

     And breadth 3*40 =120 meter.

     

    Dimensions of the field are 200 meter and 120 meter.

    4. The length of the rectangle is twice its breadth .Its area is 50 cm2 then what is the length.

    Answer-

          Lets consider breadth of Rectangle is x cm.

         Length is twice of its breadth means length is =2x cm.

       50 cm2 is the area of the rectangle given.

      2x * x =50 cm2

    2x2=50 cm2

    x2=50/2 cm2

    x2=25 cm2.

    x=√25 cm2

    x=5 cm.

    Length =2x=10cm.

    Shape of Rectangle

     Rectangle two dimensional figure of four sides. Out of four sides, opposite sides are equal and parallel . All interior angles are 90°. Diagonals are of equal length and bisect each other.
     
    Rectangle In Geometry | Properties of Rectangle| Formula and Shape of Rectangle
    Rectangle In Geometry | Properties of Rectangle| Formula and Shape of Rectangle

    Frequently Asked Questions

    1.What does rectangle mean?

    Ans: Two dimensional Quadrilateral whose two sides are equal and parallel .All interior angles are 90°. 

    2. What are the 7 properties of a rectangle?

    Ans:  7 properties of Rectangle are listed below.

    • Rectangle consists of four sides .out of four sides opposite sides are equal and parallel.
    • all angles are right angle  .
    • diagonals are in same length.
    • diagonals bisect each other.
    • A diagonal  divides the rectangle into two equal triangles.   
    • two diagonals creates four triangles after bisection in rectangle and opposite triangles formed by bisection are equal  .       
    • Adjacent sides are not equal in Rectangle.
    3. Is square a rectangle?
    Ans: If adjacent sides are equal, Then Rectangle is  a Square.

    4.What is a rectangle shape?
    Ans: Rectangle two dimensional figure of four sides. Out of four sides, opposite sides are equal and parallel .

       

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