Trapezium area


             Trapezium area:-

 Today in this article I will discuss on the topic trapezium area, hope this will help school going students a lot.To start my discussion, first I want to explain you,

    Listen full article: 


     ***What is Trapezium?

      Answer:- A quadrilateral whose any two sides are parallel is termed as trapezium.

    Trapezium area

            In the picture,

      AB∥CD of the quadrilateral ABCD
     So, ABCD is a trapezium.

    ***What is perimeter of a trapezium?

    Answer:- The perimeter of a trapezium is total surrounding spaces covered by a trapezium,but in simple words we can say that sum of all four sides of a trapezium is its perimeter.
    So, perimeter of a trapezium is = Sum of its all four sides.

    Now, we will solve

    **some problems based on perimeter of trapezium:-

    (1) If four sides of a trapezium are 6cm,4cm,3cm and 5 cm, then find the perimeter of the trapezium?

    Answer:- Here,
        1st side of the trapezium(a)=6cm
         2nd side of the trapezium(b)=4cm
         3rd side of the trapezium(c)=3cm

    4th side of the trapezium(d)=5cm
    ∴Perimeter of the trapezium=a+b+c+d

    (2)If three sides of a trapezium measures 5m,6m, 4m and the perimeter of the trapezium is 30m, then find fourth side of the trapezium.

    Answer:- 1st method:-

       Perimeter of the trapezium = 30m
    1st side of the trapezium(a)=5m 
    2nd side of the trapezium(b)=6m
    3rd side of the trapezium(c)=4m
    Let , the 4th side of the trapezium= dm
    Now, according to question,
    => 5+6+4+d=30
    ∴ The 4th side of the trapezium(d)=15m

    2nd method:-

          ∵ Perimeter of the trapezium = 30m
     and sum of its three sides =(5+6+4)cm
    let, the 4th side od the trapezium=d m
    ∴ 4th side of the trapezium(d)=(30-15)cm
                                                   =15 cm

    Now I will discuss on ,

    ***What is trapezium area?


    The area of a trapezium means total space occupied by a trapezium inside its sides i.e; all the inside space  coverd by its four sides ,The formula of trapezium area is given by

    Trapezium area

    Area of trapezium= ½ (a+b)×h
             a= 1st parallel side of the trapezium
            b= 2nd parallel side of the trapezium
            h= height of the trapezium

    Some problems related on trapezium area:-

    ***(i) If two parallel sides of a trapezium are 4cm,6cm respectively and height is 3cm, find the area of the trapezium.

    Trapezium area


            ∵1st parallel side of the trapezium(a)= 4cm 
    and 2nd parallel side of the  trapezium(b)=6cm
    also height of the trapezium(h)= 3cm
    ∴ Area of the trapezium=½(a+b)×h
                                      =5×3 cm²
                                      =15 cm²

    ***(ii) The area of a trapezium is 50 cm²,its height is 5cm, one parallel side is 6cm, find the other parallel side.

    Answer:- The area of trapezium = 50 cm²
                     height of the trapezium(h)=5cm
                   one of its parallel side (a)= 6cm
                       Let, other parallel side = b cm
                       Now, according to question,
                       ½×h(a+b) = 50
                      =>½× 5 (6+b) = 50
                      =>(6+b) =(50×2)÷5
                      => 6+b =100/5

                      => 6+b =20

                      => b =20-6

                      => b =14
    ∴ Other  parallel side of the trapezium(b)= 14cm

    ***(iii) From the given picture find the area of the shape.

    Trapezium area  


    Solution:- Given shape consists with two trapezium (at the top and at the bottom) and a rectangle in the middle.
     In case of rectangular part,
      Length of the rectangle(l)=50cm
      breadth of the rectangle(b)=10cm
    ∴ Area of the rectangular part = l × b

    =500 cm²

       Incase of trapezium part,
      1st parallel side of the trapezium(a)=30cm
    2nd parallel side of the trapezium(b)=10cm
      Height of the trapezium (h) =(70-50)cm
    ∴ Area of trapezium part =½×h×(a+b)
                                           =½ × 20×(30+10)
                                           =(10×40) cm²
                                           = 400 cm²

    Now, The are of the given shape = 2×Area of the trapezium part +Area of rectangular part

               = (2×400 + 500) cm²
               =(800+500) cm²
               = 1300cm²

    ****(iv)If two parallel sides of a trapezium are 5m and 3m also its area 30m² find the height of the trapezium.



        1st parallel side(a) of the trapezium=5m
       2nd parallel side(b) of the trapezium=3m
         Arra of the trapezium =30m²
    Let, the height of the trapezium = h m
    According to question,

    Click Now

    What is area formula of a scalene triangle?

    Answer:-The area formula of a scelene triangle = √s(s-a)(s-b)(s-c) where,s = half/semi perimeter of the triangle , and a b and c are its different sides.

    What is rhombus area formula ?

    Answer:- Rhombus area formula = 1/2 × d₁× d₂,where d₁ = 1st diagonal of the rhombus.and d₂ = 2nd diagonal of the rhombus.

    What is circle area formula ?

    Answer:- Circle area formula = πr², where r = Radius of the circle.

    What is minor sector area formula of a circle ?

    Answer:- The minor sector area formula of a circle = πr²θ/360°,Where r = radius of the circle and θ = angle subtended by the radius at center of the circle.

    What is minor segment area formula of a circle?

    Answer:- The minor segment area formula of a circle = 1/2 r²(πθ/360°- Sinθ)Where,r=radius of the circle,θ = angle subtended by the chord of the circle.

    What is the area formula of a square?

    . Answer:- The area formula of a square = a² where, a = Each side of the square

    Share this post:--