High School Math : How to find the area of a rhombus

Study concepts, example questions & explanations for High School Math

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Example Questions

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

This figure is a rhombus with a side of 8 in.Rhombus

What is the area of the rhombus (in2)?

Possible Answers:

Not enough information

Correct answer:

Not enough information

Explanation:

In order to determine the area of a rhombus you either need a base and a height OR the length of the two diagonals OR the base and an angle.  Because we are only given the base with no information about the height, there is not enough information to determine the area of the rhombus.

Example Question #2 : How To Find The Area Of A Rhombus

Find the area of the following rhombus:

Screen_shot_2014-03-01_at_8.57.04_pm

The perimeter of the rhombus is .

Possible Answers:

Correct answer:

Explanation:

The formula for the perimeter of a rhombus is:

Where  is the length of the side

Plugging in our values, we get:

 

The formula for the area of a rhombus is:

Where  is the length of one diagonal and  is the length of another diagonal

By drawing the diagonals, we create a right triangle with the hypotenuse as  and the side as .

Since we know that  is a phythagorean triple, we can infer that the third side is .

Plugging in our values, we get:

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