Maharashtra State BoardSSC (English Medium) 8th Standard
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Area of a Rhombus

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Topics

description

  • Area of the rhombus if base and height are given.
  • Area of the rhombus if the diagonals are given.

formula

  • Area of a rhombus = `1/2` x product of lengths of diagonals.

notes

Area of a Rhombus:

A rhombus can be split into two triangles by drawing one of its diagonals. This "triangulation" helps us to find a formula for the area of a rhombus.

ABCD is a rhombus. Therefore, its diagonals are perpendicular bisectors of each other.

Area of rhombus ABCD = (area of ∆ ACD) + (area of ∆ ABC)

= `(1/2 xx "AC" xx "OD") + (1/2 xx "AC" xx "OB")`

= `1/2 xx "AC" xx ("OD" + "OB")`

= `1/2 xx "AC" xx "BD"`

= `1/2` × d1 × d2

where AC = d1 and BD = d2

In other words, area of a rhombus is half the product of its diagonals.

Example

Find the area of a rhombus whose diagonals are of lengths 10 cm and 8.2 cm.

Area of the rhombus = `1/2` d1d2 where d1, d2 are lengths of diagonals.

= `1/2` × 10 × 8.2 cm2
= 41 cm2.

Example

The area of a rhombus is 240 cm2 and one of the diagonals is 16 cm. Find the other diagonal.
Let length of one diagonal d1 = 16 cm and
length of the other diagonal = d2
Area of the rhombus = `1/2` d1.d2 = 240
So, `1/2` 16 d2 = 240
Therefore, d2 = 30 cm
Hence the length of the second diagonal is 30 cm.
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