Question

In a parallelogram ABCD, AE is perpendicular to DC and CF is perpendicular to AD. If AB = 10 cm, AE = 6 cm and CF = 8 cm, then find AD.

Answer 1

Area of parallelogram = base × height
AB = 10cm
AE = 6cm
CF = 8cm
AD = ???
AB × AE = CF × AD
10 × 6 = 8 × AD
60 = 8AD
AD =60÷8
AD = 7.5 cm

Hope it helps you.

Answer 2

Given:

ABCD is a parallelogram.
AB = 10cm = DC
AE = 6 cm
FC = 8cm

Here, we have two heights here.
AE is height when DC is base,
Similarly, FC is height when AD is base.

Area of ABCD = height × base

Therefore you can say that
Area of ABCD = AB × AE = FC × AD

Now, substitute values for your terms,

And you'll get

10 × 6 = 8 × AD
60/8 = AD
AD = 7.5 cm


Therefore, AD= 7.5 cm