# ISEE Lower Level Quantitative : How to find a parallelogram on a coordinate plane

## Example Questions

### Example Question #1 : Geometry

The parallelogram shown above has a height of  and a base of length . Find the area of the parallelogram.

square units

square units

square units

square units

square units

Explanation:

To find the area of the parallelogram apply the formula:

Since, the paralleogram has a base of  and a height of  the solution is:

### Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

The parallelogram shown above has a height of  and a base of length . Find the perimeter of the parallelogram.

Explanation:

In order to find the correct perimeter of the parallelogram apply the formula: , where  the length of one of the diagonal sides and  the length of the base.

In order to find the length of side , apply the formula: . By drawing an altitude from point  to , a right triangle is formed with a base that has a length of  and a height of .

Thus, the solution is:

length of side

Therefore,

### Example Question #3 : How To Find A Parallelogram On A Coordinate Plane

Identify the coordinate points for the parallelogram that is shown above.

Explanation:

In order to identify the coordinate points for this parallelogram, notice that there must be two different pairs of coordinates with the same  values.

Thus, the parallelogram has coordinate points:

### Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

What is the area of the parallelogram shown above?

square units

square units

square units

square units

square units

Explanation:

To find the area of the parallelogram that is shown, apply the formula:
Since the parallelogram has a base of  and a height of  the solution is:

### Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

Given that the above parallelogram has base sides with a length of  and diagonal sides with a length of  what is the perimeter of the parallelogram?

Explanation:

In order to find the perimeter of the parallelogram apply the formula: , where  the length of one diagonal side and  the length of one base.

In this problem,  and .

### Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

Identify the coordinate points for the parallelogram shown above.