Area of Rhombus

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gmatusa2010: Master | Next Rank: 500 Posts; Posts: 134; Joined: Sun Jul 25, 2010 5:22 am; Thanked: 1 times; Followed by:2 members

Area of Rhombus

by gmatusa2010 » Sat Nov 20, 2010 9:21 pm

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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Source: Beat The GMAT — Problem Solving | Sat Nov 20, 2010 9:21 pm

shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 am; Location: Bangalore, India; Thanked: 146 times; Followed by:24 members

by shovan85 » Sat Nov 20, 2010 9:38 pm

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)

Of course, you can use the general formula of Parallelogram to find the area of Rhombus.
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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