# ISEE Lower Level Quantitative : Geometry

## Example Questions

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### 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 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 : Geometry

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 #1 : 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 : Geometry

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 : Geometry

Identify the coordinate points for the parallelogram 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 correct set of coordinates is:

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

A shape is plotted on a coordinate axis. The endpoints are . What shape is it?

Triangle

Rectangle

Trapezoid

Square

Parallelogram

Rectangle

Explanation:

Plot the points on a coordinate axis. Once it's graphed, you can see that there are two pairs of congruent, or equal, sides. The shape that best fits these characteristics is a rectangle.

### Example Question #2 : How To Find A Rectangle On A Coordinate Plane

Rectangle  has coordinates: ,. Find the area of rectangle .

square units

square units

square units

square units

square units

Explanation:

In order to find the area of rectangle  apply the formula:

Since rectangle  has a width of  and a length of  the solution is:

square units

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

Rectangle  has coordinates: ,. What is the perimeter?

Explanation:

To find the perimeter of rectangle , apply the formula:

Thus, the solution is:

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

Rectangle  has coordinate points: . Find the area of rectangle

square units

square units

square units

square units

square units

Explanation:

The area of rectangle  can be found by multiplying the width and length of the rectangle.

To find the length of the rectangle compare the x values of two of the coordinates:

Since  the length is .

To  find the width of the rectangle we need to look at the y coordinates of two of the points.

Since  the width is .

The solution is:

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