Q:

Total distance travelled in velocity-time graph

I figured out by using trapezium rule. Any other method to find out the total distance travelled by the car ?

A:

Since the distance travelled is equal to the area under the curve (or more generally, the area between the curve and the time-axis), you have the right idea.
It's very rare that you are given such edgy graphs though, since it is virtually impossible to have travelled in such a manner. The traveler on the graph has obtained speed and come to stops instantaneously, which, as you probably know, can't happen in real life.
But on to your question...
Say the graph was smooth. It would be impossible to use rectangles and trapezoids to calculate the area. At best, you could maybe make some estimates, but rarely find an exact answer. When you move on to calculus, you'll be learning about integrals - more specifically definite integrals - which we use to calculate the area given smoother graphs.

