MathematicsFind the area of the trapezium in terms of x, and if BCD = y  , then calculate the value of y. 

Find the area of the trapezium in terms of x, and if BCD = y  , then calculate the value of y.
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  1. A
    105 x 2 sq.cm, 22.61  
  2. B
    125 x 2 sq.cm, 34.51  
  3. C
    235 x 2 sq.cm, 63.41  
  4. D
    456 x 2 sq.cm, 87.31  

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    Solution:

    Let’s divide the field into two triangles ADF, BCE, and one rectangle ABEF.
    Now, find the area of the triangle by using the formula A= 1 2 ×b×h  .
    Area of ADF= 1 2 ×DF×AF = 1 2 ×4x×5x = 20 x 2 2 =10 x 2 sq.cm.  
    Area of BCE= 1 2 ×CE×BE = 1 2 ×12x×5x = 60 x 2 2 =30 x 2 sq.cm.  
    Now, calculate the value of the area of the rectangle by using the formula A=l×b  .
    Area of ABEF=AB×BE =13x×5x =65 x 2 sq.cm.  
    Area of the trapezium ABCD = Area of triangle ADF+Area of triangle BCE+Area of rectangle ABEF =10x 2 +65x 2 +30x 2 =105x 2 sq.cm  
    To find the value of y, in right angled triangle at angle E, we have
    tany= opposite adjacent = BE CE = 5x 12x = 5 12 y= tan 1 5 12 y= 22.61  
    Hence, the correct option is 1.
     
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