ISEE Upper Level Math : How to find the area of a rhombus

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

Example Question #1 : Rhombuses

Two diagonals of a rhombus have lengths of  and . Give the area in terms of .

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a rhombus is

,

where is the length of one diagonal and is the length of the other diagonal.

 

 

Example Question #2 : Rhombuses

A rhombus has side length , and one of the interior angles is . Give the area of the rhombus.

 

Possible Answers:

Correct answer:

Explanation:

The area of a rhombus can be determined by the following formula:

,

where is the length of any side and is any interior angle. 

 

Example Question #1 : How To Find The Area Of A Rhombus

Find the area of a rhombus with one diagonal having a length of 12in and the other having a length two times the first diagonal.  

Possible Answers:

Correct answer:

Explanation:

To find the area of a rhombus, we will use the following formula:

where p and q are the lengths of the diagonals of the rhombus.

 

Now, we know one diagonal has a length of 12in.  We also know the other diagonal is two times the first diagonal.  Therefore, the second diagonal is 24in.

Knowing this, we can substitute into the formula.  We get

 

 

 

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