ABCD is a parallelogram. AE is perpendicular on DC and CF is perpendicular on AD.

If AB = 10 cm, AE = 8 cm and CF = 12 cm. Find AD.

Let us start by finding the area of parallelogram ABCD

If we consider DC as the base of the parallelogram the height will be AE

Area of parallelogram = base × height

⇒ area of parallelogram ABCD = DC × AE

Given is AB = 10 cm

As it is a parallelogram opposite sides are equal i.e. DC = 10 cm

AE = 8 cm …(given)

Therefore, area of parallelogram ABCD = 10 × 8 = 80 cm²

As for the same shape area won’t change even if we find area by other terms

Now consider AD as the base of parallelogram ABCD then the height will be FC

Area of parallelogram = base × height

⇒ area of parallelogram ABCD = AD × CF

CF = 12 cm …(given)

⇒ 80 = AD × 12

⇒ AD = =

Therefore, AD = 6.67 cm