Question

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

पर्याय

•  12 cm²

•  20 cm²

• 24 cm²

•  36 cm²

Answer 1

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`