Finding area of paralellogram

Let It Fall · #1 11-12-2009, 01:51 AM

I know this is an easy one. Base x height

However I can't stand memorizing formulas and basically goes by what makes sense, after two years out of school I ran across this and immediatly did base x diagonal height.

This is wrong but why? Can someone explain this to me?

In my mind if you were to straighten the diagonal sides to make a box, the area inside would stay the same and you would use the previously diagonal measurement.

Using example below let's say base is 12" height is 4" and diagonal is 5"

**bassybill** · #2 11-12-2009, 01:57 AM

The area would not stay the same if you straightened the box to rectangular - it would increase. The height would now be 5 instead of 4.

To see this if you don't get it, think about doing the reverse. If you squashed it, instead of straightening it, the area would decrease (to zero, if totally flat).

The diagram gives you a clue as to why the base x height formula works. HINT - try adding the area of the rectangle in the middle to the areas for the two triangles either side. Or just think about cutting the right triangle off and sticking it back on to the left hand side.

Let It Fall · #3 11-12-2009, 02:10 AM

Aha! I got it now thanks! Sometimes you have to think of extremes and when you mentioned squashing it, it made sense instantly, the area would decrease! Thanks for the help, I now feel stupid and want to delete this thread. But now that I understand why I'll ne'er make the same mistake.

**bassybill** · #4 11-12-2009, 11:21 AM

There's nothing stupid about asking a genuine question. Happy to help.