So AD=CD

Because AD is the center line on the side of BC.

So d is the midpoint of BC.

So BD=CD

So BD=AD

So angle B= angle BAD

Because angle BAD+ angle B+ angle ACD+ angle CAD= 180 degrees.

So angle BAD+ angle CAD= angle BAC=90 degrees.

So the angle BAC=90 degrees.

2. solution: extend the extension lines of AD and BC at point e.

Because angle ADC= angle D=90 degrees

Angle ADC+ angle CDE= 180 degrees

So CDE angle =90 degrees.

So the triangle CDE is a right triangle.

Because angle A+ angle B+ angle E= 180 degrees.

Angle A=60 degrees

Angle B=90 degrees

So the angle E=30 degrees.

Triangle ABE is a right triangle.

So the S triangle ABE= 1/2BE*AB.

AB= 1/2AE

AE^2=AB^2+BE^2

Because AB=4

So AE=8

BE=4 times the root number 3.

S triangle ABE=8 times the root number 3

In the right triangle CDE, the angle CDE=90 degrees and the angle E=30 degrees.

So the S triangle CDE= 1/2CD*DE.

CD= 1/2CE

CD^2+DE^2=CE^2

Because CD=2

So CE=4

DE=2 times root number 3.

Triangle CDE=2 times root number 3.

Because s quadrilateral ABCD=S triangle ABE-S triangle CDE

So the S quadrilateral ABCD=6 times the root number 3.

Because AD=AE-DE=8-2 times the root number 3.

BC=BE-CE=4 times the root number 3-4.

The perimeter of the quadrilateral ABCD =AB+BC+CD+AD.

So the perimeter of the quadrilateral ABCD = 10+2 times the root number 3.

To sum up, the area of quadrilateral ABCD is 6 times that of root number 3, and its perimeter is 10+2 times that of root number 3.