Picture problems:-

Today in this article I will explain on picture problems which is actually based on mathematics problems and we will learn how to solve a picture problem of mathematics from a given picture,Hope these problems will help school going children a lot. Let's start,

Question (i):-Find the area of the Yellow shaded region of the picture.

Solution:

∵The above picture is made of a rectangle and a semi circle. 

To find:-The area of the Yellow 

shaded region of the picture ?

In case, of semi circle
       Radius of semi circle (r) = 7cm
∴ Area of the semi circle = ½ πr²
                                     =  (½ × 22/7×7×7)
                            [Let us assume,π=22/7]
                                    = (11×7)
                                    =77 cm²
  Now,
         In case,of rectangle,

    length of the rectangle(l) = 2×r
                                            = ( 2×7)
                                            = 14 cm
    breadth of the rectangle(b) = 9cm
∴ Area of the rectangle = l×b
                                      = 14 × 9
                                      = 126cm²
∴ Area of the yellow shaded region = Area of the rectangle - Area of the semi circle

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                         = (126 -77)cm²
                         = 49cm²

Question(ii) Find the area of the green shaded region of the picture.

Solution:

∵The above picture is made of a rectangle and a square.
To find:-The area of green shaded region of the picture  = ?
Solution:-
          In case,of rectangle,
           length(l) = 15m
           breadth(b) = 10m
v∴ Area of the rectangle = l×b
                                       = 15 × 10
                                       = 150m²
In case of square,
         Each side of the square (a) =7m
        ∴ Area of the square = a²
                                         = (7 × 7)m²
                                         = 49m²
∴ The area of green shaded region of the picture =  Area of the rectangle - Area of the square
            = (150 -49)m²
            = 101m²

 Question(iii) FInd the area of the red shaded region of the picture.

       

∵The above picture is made of two circles.

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 To find:-The area of red shaded region of the picture  = ?
 Solution: 1st method:-
      ∵ The radius of bigger circle(R)= 14cm          
    ∴ area of the bigger circle = πR²
                                              = 22/7×14×14
                                              = 22×2×14
                                              = 22×28
                                              = 616 cm²
∵ The radius of smaller circle(r)= 7cm

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∴ area of the smaller circle = πr²
            = 22/7×7×7[assuming, π=22/7]
            =22×7                                                
            = 154cm²
∴ The area of red shaded region of the picture = (616-154)
            =  462cm²

2ndmethod:-
∵ The radius of bigger circle(R)= 14cm
∵ The radius of smaller circle(r)= 7cm
 ∴The area of red shaded region of the picture = π(R²-r²)
            = 22/7(14² - 7²)[Assuming π=22/7)
    = 22/7(14+7)(14-7)[Applying identity, (a²- b²)= (a+b)(a-b)]
             =(22/7× 21 ×7)
             =(22×21)

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             =462cm²

Question(iv) Find the area of the orange shaded region of the picture.

          

∵The above picture is made of a trapezium  and a circle.
To find:-The area of orange shaded region of the picture  = ?
Solution:- 
                 In case of trapezium,
   1st parallel side(a)= 10cm
   2nd parallel side (b) = 16 cm
   height of the trapezium(h) = 10 cm
∴ Area of the trapezium = ½ ×h (a+b)
                                      =½ × 10(10+16)
                                      = 5 × 26
                                      = 130 cm²

In case of circle,
     Radius of the circle (r) = 3.5 cm
   ∴ Area of the circle = πr²
                                  = (22/7×3.5×3.5)cm²
                                  =(22×.5 ×3.5)cm²
                                  =11.0 × 3.5 cm²
                                  = 38.5cm²
∴The area of orange shaded region of the picture = Area of the trapezium -Area of the circle

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            = (130-38.5)cm²
            = 91.5cm²

Question(v) The length of the side of a rhombus is 13cm and its one of diagonal is 24cm, find the area of the rhombus.

. Solution:-

∵ Each side of the rhombus=AB=BC=CD=AD=13cm[∵All sides of a rhombus are equal]
It's longer diagonal(AC)=24cm and BD⊥AC
∵ Diagonals of a rhombus bisect each-othe perpandicularly.
∴AO =OC=½ AC = ½ ×24 cm
                             = 12cm
Now in right angled triangle AOD we get,
   ∵ OD²=AD²-AO²[∵<AOD =90°]
     

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