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Question
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`
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