Question from Karthik,

How can u " SHOW THAT THE AREA OF THE TRAPEZIUM IS EQUAL TO HALF THE PRODUCT OF ITS ALTITUDE AND THE SUM OF ITS PARALLEL SIDES." in an Innovative And Creative way.....

Hi Karthik,

Your question is on record here at Math Central for all to see, so please make sure you don't take credit for this on a homework assignment! :)

Here's a trapezium I've drawn. I drew a line through it at half the height, then drew perpendiculars bisecting the non-parallel sides. The parallel side lengths are a and b:

Now let's move things around a bit:

The bottom is now (a+b) and the height of the coloured area is half the height of the original trapezium, so the area is half the product of the trapezium's height and the sum of the lengths of its parallel sides.

Stephen La Rocque.>