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In the Given Figure, Abcd and Fecg Are Parallelograms Equal in Area. If Ar (δAqe) = 12 Cm2, Then Ar (||Gm Fgbq) = - Mathematics

MCQ

In the given figure, ABCD and FECG are parallelograms equal in area. If ar (ΔAQE) = 12 cm2, then ar (||gm FGBQ) = 

Options

  •  12 cm2

  •  20 cm2

  • 24 cm2

  •  36 cm2

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Solution

Given: (1) Area of parallelogram ABCD is equal to Area of parallelogram FECG.

(2) If Area of ΔAQE is 12cm.

To find: Area of parallelogram FGBQ

Calculation: We know that diagonal of a parallelogram divides the parallelogram into two triangles of equal area.

It is given that,

`ar ("||"^(gm)ABCD) = ar ("||"^(gm) FECG)`

`⇒ ar (ΔADE) + ar (ΔAQE) + ar ( "||"^(gm) QECB ) = ar ("||"^(gm) QECB) + ar ("||"^(gm) FQBG)`

`⇒ ar (ΔADE) + ar (ΔAQE) = ar  "||"^(gm) FQBG`

`⇒ 2ar (ΔAQE) = ar ( "||"^(gm) FQBG)`

`⇒ar ( "||"^(gm) FQBG) = 2ar (ΔAQE) `

`⇒ar ( "||"^(gm) FQBG) = 2 xx 12` 

`⇒ar ( "||"^(gm) FQBG) = 24  cm^2`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 20 | Page 62
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