The area of a trapezium becomes 4 times,

False

We know that,

Area of a trapezium = 1/2 (a + b) x h

where, a and b are the lengths of parallel sides and h is the altitude (height).

Now, if the height gets doubled, then

Area of trapezium = 1/2(a + b) x 2h = 2(1/2(a + b) x h)

Hence, the area is doubled.

So, the statement is false.