Here is the image/grid:
http://i47.tinypic.com/2e2qnau.jpg

Here are the questions:
http://i47.tinypic.com/2aj412a.jpg

If you wanted to find the area, take the triangle on the far right, place on the left side of your drawing and figure as a rectangle.
Don't know how to express mathematically. Maybe look through here:
http://www.mathsisfun.com/geometry/index.html
Here is your parrallelogram:
http://www.mathsisfun.com/area.html

http://i47.tinypic.com/2e2qnau.jpg

http://i47.tinypic.com/2aj412a.jpg

1. This is undoubtedly a parallelogram. That being said, AB and DC are parallel, and AD and BC are parallel.

So, the sum of angles BCD and ADC must equal 180 (co-interior relationship)

\angle BCD + \angle ADC = 180^{\small{o}}

2. Well, I think that should be obvious. It's a trapezium. I'll leave the explanation to you.

The area can be obtained 2 simple ways:
a. Counting the small units, 1 square is one units (like in small classes)
b. Count the number of squares along the base, the upper horizontal 'roof' and the perpendicular height (EC). The area is given by the formula:

Area = \frac12 (l_1 + l_2) h

3. Use Pythagoras' Theorem. If you have a right angled triangle, the hypotenuse a is given by:

a^2 = b^2 + c^2 (where b and c are the two other sides)

4. This part has been already answered in the first part itself... I'll let you day the explanation.

The area can be obtained 2 simple ways:
a. Counting the small units, 1 square is one units (like in small classes again)
b. Count the number of squares along the base and the perpendicular height (EC). The area is found the same way as you find the area of a rectangle:

Area = l \times h

Post your answers. :)