Question

The parallel sides of a Trapezium are 25 cm and 11 cm while its non parallel sides are 15 cm and 13 cm find the area of the trapezium.

Answer 1

Draw CE such that AECD is a parallelogram
AE = CD = 11 cm
AD = CE = 15 cm

EB = 14 cm
Area of ΔECB = s(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 = 21(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

Hope it Helps...
 

Answer 2

Answer

Hope this is helpful