Question

In a parallelogram ABCD, AB = 18 cm, BC = 12 cm. AL ⊥ DC and AM ⊥ BC.


If AL = 6.4 cm, find the length of AM.

Answer 1

Base, AB = 18 cm
Height, AL = 6.4 cm
∴ Area of the parallelogram ABCD = Base $\times$ Height
= (18 cm $\times$ 6.4 cm) = 115.2 cm² ... (i)

Now, taking BC as the base:
Area of the parallelogram ABCD = Base $\times$ Height
= (12 cm $\times$ AM) ... (ii)
From equation (i) and (ii):
12 cm $\times$ AM = 115.2 cm²
⇒ AM = $\left(\frac{115.2}{12}\right)$cm
= 9.6 cm