Question

In the given figure, ratio of AG to GH is 1:3, area of parallelogram ABFE is 10 $c{m}^2$, then find the area of parallelogram ABCD

• A. 40 $c{m}^2$
• B. 30 $c{m}^2$
• C. 80 $c{m}^2$
• D. 60 $c{m}^2$

Answer 1

The correct option is A 40 $c{m}^2$

Given: ABCD and ABFE is a parallelogram hence AB=FE=CD and are parallel to each other
$\frac{AG}{GH}$ = $\frac{1}{3}$ $⟹$ GH = 3(AG)

we know,
AH = AG + GH = AG + 3(AG) = 4(AG)

Area of parallelogram = base$\times$height
$\frac{\text{Area of ABFE}}{\text{Area of ABCD}}$ = $\frac{EF\times AG}{CD\times AH}$ = $\frac{AG}{4\left(AG\right)}$ = $\frac{1}{4}$

$⟹$Area of ABCD=4$\times$(Area of ABFE)
$\therefore$ area of ABCD = 4$\times$10 = 40 $c{m}^2$