Wire tessellation of an isosceles-triangle trapezium

Twelve identical isosceles triangles, each with base \(x\) cm and equal sides \(y\) cm, tessellate the trapezium shown. The outer boundary consists of six \(x\)-segments and four \(y\)-segments, while the complete wire network contains nine \(x\)-segments and fourteen \(y\)-segments. The outer perimeter is \(54\) cm and the total wire length is \(126\) cm.

1. Form two equations and find \(x,y\).
2. Hence find the trapezium area.