### All ISEE Lower Level Quantitative Resources

## Example Questions

### Example Question #1 : Coordinate Geometry

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

**Possible Answers:**

square units

square units

square units

square units

**Correct answer:**

square units

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 #2 : Coordinate Geometry

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

**Possible Answers:**

**Correct answer:**

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 : Coordinate Geometry

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

**Possible Answers:**

**Correct answer:**

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 #4 : Coordinate Geometry

What is the area of the parallelogram shown above?

**Possible Answers:**

square units

square units

square units

square units

**Correct answer:**

square units

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 #5 : Coordinate Geometry

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?

**Possible Answers:**

**Correct answer:**

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 .

Thus, the correct answer is:

### Example Question #6 : Coordinate Geometry

Identify the coordinate points for the parallelogram shown above.

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

Rectangle

Trapezoid

Triangle

Square

Parallelogram

**Correct answer:**

Rectangle

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 .

**Possible Answers:**

square units

square units

square units

square units

**Correct answer:**

square units

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 #3 : How To Find A Rectangle On A Coordinate Plane

Rectangle has coordinates: ,, , . What is the perimeter?

**Possible Answers:**

**Correct answer:**

To find the perimeter of rectangle , apply the formula:

Thus, the solution is:

### Example Question #4 : How To Find A Rectangle On A Coordinate Plane

Rectangle has coordinate points: , , , . Find the area of rectangle .

**Possible Answers:**

square units

square units

square units

square units

**Correct answer:**

square units

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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