# Consider a parallelogram, ABCD. AE is perpendicular to DC and CF is perpendicular to AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, Find AD.

A parallelogram is a quadrilateral, whose opposite sides are parallel and equal to each other,

## Answer: For a parallelogram ABCD, where AE is perpendicular to DC and CF is perpendicular to AD with AB = 16 cm, AE = 8 cm and CF = 10 cm the value of AD is 12.8 cm.

Let's draw a diagram of parallelogram ABCD then find AD

**Explanation:**

Below is the given diagram of parallelogram ABCD based on the question

AE = 8cm (given)

CF = 10cm (given)

AB = DC = 16cm (Since, opposite sides of a parallelogram are equal)In a parallelogram, we know that opposite sides are equal)

Now, to calculate the value of AD

We know that,

**Area of parallelogram = b × h **(where b = base, h = height)

DC × AE = AD × FC

=> 16 × 8 = AD ×10 (By substituting all the values)

=> 128 = 10AD

=> AD = 12.8 cm