Given, side AB || side DC.
l(AB) = 9 cm, l(AE) = 10 cm,
A(ABCD) = 115 cm²
∴ ABCD is a trapezium.
Area of a trapezium
= (1/2) x sum of lengths of parallel sides x height
∴ A(ABCD) = (1/2) x [l(AB) + l(DC) x l(AE)]
∴ 115 = (1/2) x [9 + l(DC)] x 10
∴ (115 x 2)/10 = 9 + l(DC)
∴ 23 = 9 + l(DC)
∴ l(DC) = 23 – 9
∴ l(DC) = 14cm