ISEE Upper Level Math : How to find the area of a parallelogram
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Example Questions
Example Question #1 : How To Find The Area Of A Parallelogram
Give the area of the above parallelogram if 
Multiply height 
By the 30-60-90 Theorem:
and
The area is therefore
Example Question #2 : How To Find The Area Of A Parallelogram
Give the area of the above parallelogram if 
Multiply height 
By the 45-45-90 Theorem,
The area is therefore
Example Question #54 : Quadrilaterals
Three of the vertices of a parallelogram on the coordinate plane are 
Insufficient information is given to answer the problem.
As can be seen in the diagram, there are three possible locations of the fourth point of the parallelogram:
Regardless of the location of the fourth point, however, the triangle with the given three vertices comprises exactly half the parallelogram. Therefore, the parallelogram has double that of the triangle.
The area of the triangle can be computed by noting that the triangle is actually a part of a 12-by-12 square with three additional right triangles cut out:
The area of the 12 by 12 square is
The area of the green triangle is 
The area of the blue triangle is 
The area of the pink triangle is 
The area of the main triangle is therefore
The parallelogram has area twice this, or 
Example Question #2 : Parallelograms
One of the sides of a square on the coordinate plane has an endpoint at the point with coordinates 
The length of a segment with endpoints 
This is the length of one side of the square, so the area is the square of this, or 41.
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