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The parallel sides of a trapezium are 25cm & 11cm,while its non parallel sides are 15cm & 13cm,Find the area of trapezium?

The parallel sides of a trapezium are 25cm & 11cm,while its non parallel sides are 15cm & 13cm,Find the area of trapezium?

Grade:10

1 Answers

Arun
25757 Points
5 years ago
Dear student
 
 
Draw CE such that AECD is a parallelogram
AE = CD = 11 cm
AD = CE = 15 cm

EB = 14 cm
Area of ΔECB = \sqrts(s-a)(s-b)(s-c)
where s = (a+b+c)/2
a = 13 cm, b = 14 cm, c = 15 cm
Here s = (13+14+15)/2 = 21 cm
Area of ΔECB = \large \sqrt21(21-13)(21-14)(21-15)
     
= 84 sq cm
 But Area of ΔECB = 1/2 × base (EB) × height (h)

1/2 × 14 × h = 84

h = 12 cm

Area of trapezium ABCD = 1/2 × h × (AB + CD)
 
                                         = 1/2 × 12 × (25 + 11) 
         
                                         =  6 × 36
  
                                         = 216 sq cm
 
Regards
Arun (askIITians forum expert)

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