A paper has the precise shape of a triangle which is denoted by ABC, with AB = BC = CA = x (say) and, D is a point on BC.

Vertex A is joined onto D forming the crease EF - where E is on AB and F is on AC.

Given that DF is perpendicular to BC, determine:

1. The length of EF in terms of x.
2. The area of each of the triangles BED, DEF and DFC in terms of x.