Question

Match the parallelograms to the measurements of the corresponding missing sides.

• A. 8 cm
• B. 12.8 cm
• C. 9 cm

Answer 1

$\text{Area of a parallelogram}=\text{base}\times \text{corresponding height}$
In the first parallelogram, AB = 16 cm, AE = 8 cm and CF = 10 cm.
Area = b $\times$ h = AB $\times$ AE
$⟹\text{Area}=16\times 8=128{\text{cm}}^2$
Also, Area = AD $\times$ CF
$\Rightarrow$ 128 = AD $\times$ 10
$\Rightarrow$ AD = 12.8 cm

In the second parallelogram, area = 128${\text{cm}}^2$ and CF = 16 cm.
Area = b $\times$ h = AD $\times$ CF
$⟹128=AD\times 16$
$\Rightarrow$ AD = 8 cm
But, AD = BC = 8 cm.

In the third parallelogram, DC = 12 cm, AD = 8 cm and AE = 6 cm.
Area = b $\times$ h = DC $\times$ AE
Area = 12 $\times$ 6 = 72 $c{m}^2$
Also, Area = AD $\times$ CF
$\Rightarrow$ 72 = 8 $\times$ CF
$\Rightarrow$ CF = 9 cm