SSAT Middle Level Math : Geometry

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

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

A square has an area of  square units, what is the perimeter of the square? 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, apply the formula , in order to conclude that the length of side  must equal  for the area to equal 

Once you've found the length of side , apply the formula 


Example Question #31 : Coordinate Geometry

A square has an area of  square units. Find the perimeter. 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, apply the formula , in order to conclude that the length of side  must equal  for the area to equal 

Once you've found the length of side , apply the formula 

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

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Find the area of the above square. 

Possible Answers:

 

 

 

 

Correct answer:

 

Explanation:

In order to find the area of the square above apply the formula: , where  the length of one side of the square. 

Since 
the solution is 

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

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Find the area of the square shown above. 

Possible Answers:

 

 

 

Correct answer:

 

Explanation:

In order to find the area of the above square, apply the formula: , when  equals the length of one side of the square. 

Since,  the solution is:



Make sure to attach "square units" to your answer! 

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

 

Parellelogram

NOTE: Figure NOT drawn to scale.

What is the area of the parallelogram represented by the above figure?

Possible Answers:

Correct answer:

Explanation:

The area of a parallelogram is its base multiplied by its height. The diagram below shows both in green:

Parellelogram

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

Triangle5

Find the area of the above parallelogram given a height of 5 units, as shown to scale.

Possible Answers:

Correct answer:

Explanation:

Since the diagram is drawn to scale, the base of the parallelogram must be 6 units in length. Using the area formula for a parallelogram:

 

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

Triangle5

Given a base of 12 units and an area of 120 square units, find the height of the paralellogram shown above.

Possible Answers:

Correct answer:

Explanation:

The area formula for a parallelogram is:

Thus, to find the height, rearrange:

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

Triangle5

The above parallelogram has an area of 30 square units. Which of the following could be the lengths of the base and height of this figure? (Image not drawn to scale.)

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a parallelogram is:

Thus, the base and height must equal 30 square units when multiplied together.

 

3 and 10 are the only combination of base and height which, when multiplied, equal the area of 30 square units.

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

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In the above figure Dr. Robinson's shed is represented by the red square, and the shed has a perimeter of  yards. Find how much area Dr. Robinson has in his backyard--excluding the area that the shed occupies.   

Possible Answers:

 

 

 

 

Correct answer:

 

Explanation:

To find how much area Dr. Robinson has around his shed in his backyard, first apply the formula: , where  represents one side of the red shed. Given that
 must equal  because .

Now you have enough information to find the area of the red shed.
Apply the formula: 


Since the rectangular fence has a width of  yards and a length of  yards, apply the formula:  in order to find the area of the entire backyard. 
Thus, 


Then simply find the difference between the area of the entire yard and the area of the shed. 

Thus the final solution is:

  

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

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Identify the correct set of coordinates for rectangle .

Possible Answers:

Correct answer:

Explanation:

To identify the correct set of coordinate points for rectangle , note that the correct set must have two sets of matching  coordinates and two sets of matching  coordinates. The only answer choice that meets these specifications is:

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