Answer :

Given:


AB (say) = 11 cm


DC (say) = 25 cm


AD (say) = 15 cm


BC (say) = 13 cm


Draw AE BC



Now the trapezium is divided into a triangle ADE and a parallelogram AECB.


Since, AECB is a parallelogram


Therefore, AE = BC = 13 cm


And, AB = EC


DE = DC – EC( = AB) = 25 – 11 = 14 cm


Now,


We know that,


Area of a scalene triangle (∆AED) = √(s(s-AE)(s-ED)(s-AD))


Where,




s = 21 cm


Now,


Area of a scalene triangle = √(21cm × (21-13)cm × (21-14)cm × (21-15)cm)


= √(21cm × 8cm × 7cm × 6cm)


= √7056 cm2


= 84 cm2


Also,


Area of a triangle = 1/2 × base × height


84 = 1/2 × 14 × height



height = 12 cm


Now,


Area of a parallelogram = base × height


= 11 cm × 12 cm


= 132 cm2


Now,


Area of Trapezium ABCD = Area of ∆ADE + Area of a parallelogram ABCE


= 84 cm2 + 132 cm2


= 216 cm2


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