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
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.