ISEE Lower Level Quantitative : Geometry

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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Example Questions

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Example Question #1 : Geometry

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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

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

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

Possible Answers:

Correct answer:

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

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

Possible Answers:

Correct answer:

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

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What is the area of the parallelogram shown above? 

Possible Answers:

 square units

 square units

 square units

 square units

Correct answer:

 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 : Geometry

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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:

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 .
Thus, the correct answer is: 

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

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Identify the coordinate points for the parallelogram shown above. 

Possible Answers:

Correct answer:

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?

Possible Answers:

Parallelogram

Triangle

Rectangle

Trapezoid

Square

Correct answer:

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

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

Possible Answers:

 square units

 square units

 square units

 square units

Correct answer:

 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 : Geometry

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Rectangle  has coordinates: ,. What is the perimeter?

Possible Answers:

Correct answer:

Explanation:

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

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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