SSAT Middle Level Math : How to find a rectangle on a coordinate plane

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

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Example Questions

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 #2 : 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:

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

Dr. Robinson recently put a rectangular fence around his backyard. The fence has a width of  yards and a length of  yards. If Dr. Robinson paid  for every yard of fence, how much did the fence cost? 

Possible Answers:

Correct answer:

Explanation:

To find the cost of the fence, apply the formula  in order to first find the length of the perimeter of the fence.

Then multiply the perimeter by .

Thus, the solution is:





 

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

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The rectangle shown above has a width of  and a length of . Find the area and perimeter of the rectangle. 

Possible Answers:

Correct answer:

Explanation:

To solve this problem apply the formulas:  & 

Thus, the solution is:


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