Question

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

Answer 1

Area of trapezium is 216 m².please see the attachment

Answer 2

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

EB = 14 cm
Area of ΔECB = $\sqrt{s(s-a)(s-b)(s-c)}$ 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 = $\sqrt{21(21-13)(21-14)(21-15)}$ 
     
= $\sqrt{21(8)(7)(6)}$ 
= 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