1. Prove that ABCD is a parallelogram, so angle ABC= angle ADC, let AE be vertical BC to E, and AF be vertical DC to F. Because the width of two pieces of paper is the same, AE=AF, because angle ABC= angle ADC and angle AEB= angle AFD, all triangles AEB are equal to triangle AFD, so AB=AD, so) quadrilateral ABCD is a diamond.

Area =2

2. connect AF and EB. Because AE is parallel to FC, angle AEF= angle F, angle EAG= angle FBA, and because public side AB and triangle AEB are all equal to triangle AFB, AE is equal to FB, and because AD is parallel to FB and AEBF is a parallelogram, AB and EF are equally divided.