Draw CE such that AECD is a parallelogram
AE = CD = 11 cm
AD = CE = 15 cm
EB = 14 cm
Area of ΔECB = [tex] \sqrt{s(s-a)(s-b)(s-c)} [/tex] 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 = [tex] \sqrt{21(21-13)(21-14)(21-15)} [/tex]
= [tex] \sqrt{21(8)(7)(6)} [/tex]
= 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
