Area of Rhombus
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I know that a rhombus is a subset of the parallelogram does that mean you can apply the area formula of the parallelogram to a rhombus? The official formula of the area of a rhombus is (Diagonal 1 x Diagonal2)/ 2. However, I recently ran across a problem that suggests you can apply the area of a parallelogram to the rhombus because it is a subset of a parallelogram. Is this true? (Squares and rectangles are parallelograms, and all three have the same formula)
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Of course, you can use the general formula of Parallelogram to find the area of Rhombus.gmatusa2010 wrote:I know that a rhombus is a subset of the parallelogram does that mean you can apply the area formula of the parallelogram to a rhombus? The official formula of the area of a rhombus is (Diagonal 1 x Diagonal2)/ 2. However, I recently ran across a problem that suggests you can apply the area of a parallelogram to the rhombus because it is a subset of a parallelogram. Is this true? (Squares and rectangles are parallelograms, and all three have the same formula)
Formula: Area = height * base.
The reason that this formula can be written as (Diagonal 1 x Diagonal2)/ 2, the diagonals of the Rhombus bisect each other perpendicularly.
See the Rhombus ABCD.
Area of ABCD
= Area of triangle ABD + Area of triangle BCD
= [ (1/2) * AO * BD ] + [ (1/2) * OC * BD]
= (1/2) * BD (AO + OC)
= (1/2) * BD * AC (BD and AC are diagonals of ABCD)
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