Question

In ABCD, side AB || side DC, seg AE ⊥ seg DC. If l(AB) = 9 cm, l(AE) = 10 cm, A(ABCD) = 115 cm², find l(DC).

Answer 1

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