# Areas of parallelogram

Given: Let ABCD be a parallelogram. Let AE be the altitude from A to side CD.

To Prove: Area of parallelogram ABCD = CD x AE

Proof:

From fig, we can see that,

Area of parallelogram ABCD = Area of triangle ADC + Area of triangle ABC

= (1/2 x CD x AE) + (1/2 x AB + CF)

Now, we know that the distance between two parallel lines is always constant and also AB = CD here.

So, we can say that CF = AE

= 1/2 x CD x AE + 1/2 x CD x AE (Since CF = AE)

= CD x AE Proved

Hence, area of parallelogram is equal to base into height.