How to find the area of a rhombus - High School Math
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This figure is a rhombus with a side of 8 in.
What is the area of the rhombus (in2)?
This figure is a rhombus with a side of 8 in.
What is the area of the rhombus (in2)?
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.
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.
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Find the area of the following rhombus:
The perimeter of the rhombus is 
.
Find the area of the following rhombus:
The perimeter of the rhombus is
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:
The formula for the perimeter of a rhombus is:
Where
Plugging in our values, we get:
The formula for the area of a rhombus is:
Where
By drawing the diagonals, we create a right triangle with the hypotenuse as
Since we know that
Plugging in our values, we get:
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