Rhombuses - High School Math
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A quadrilateral ABCD has diagonals that are perpendicular bisectors of one another. Which of the following classifications must apply to quadrilateral ABCD?
I. parallelogram
II. rhombus
III. square
A quadrilateral ABCD has diagonals that are perpendicular bisectors of one another. Which of the following classifications must apply to quadrilateral ABCD?
I. parallelogram
II. rhombus
III. square
If the diagonals of a quadrilateral are perpendicular bisectors of one another, then the quadrilateral must be a rhombus, but not necessarily a square. Since all rhombi are also parallelograms, quadrilateral ABCD must be both a rhombus and parallelogram.
If the diagonals of a quadrilateral are perpendicular bisectors of one another, then the quadrilateral must be a rhombus, but not necessarily a square. Since all rhombi are also parallelograms, quadrilateral ABCD must be both a rhombus and parallelogram.
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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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This figure is a rhombus with a side of 8 in.
What is the perimeter of the rhombus (in)?
This figure is a rhombus with a side of 8 in.
What is the perimeter of the rhombus (in)?
The perimeter of the rhombus is the distance around the outside of the figure. Since a rhombus has 4 congruent sides, the perimeter is simply 
.
The perimeter of the rhombus is the distance around the outside of the figure. Since a rhombus has 4 congruent sides, the perimeter is simply
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You are given a rhombus with a side of 
meters. What is the perimeter of the rhombus?
You are given a rhombus with a side of
A rhombus is a quadrilateral (
sided figure) with 
congruent sides. The perimeter is the sum of the sides. Thus, to find the perimeter of the rhombus, we multiply the perimeter by 
. This gives us 
meters.
A rhombus is a quadrilateral (
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