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### Using a Parallelogram to find the Area of a Triangle

```
Date: 06/26/2001 at 18:58:46
From: Christy V.
Subject: Math/area

What is the area of a triangle with a height of 12 inches and a base
of 3 inches?

I tried it myself, but I just don't get it.
```

```
Date: 06/27/2001 at 17:12:03
From: Doctor Ian
Subject: Re: Math/area

Hi Christy,

Here's a way that you can figure this out when you've forgotten the
formula.

First, draw the triangle.

.
. .   |
.   .    | 12
.     .     |
.........      |
3

Now draw a mirror image of the triangle, reflected across one side:

.........
.     . .   |
.   .   .    | 12
. .     .     |
.........      |
3

Now you have a parallelogram, so the area of the triangle must be
exactly half the area of this parallelogram.

But what is the area of a parallelogram? Well, we can do a similar
trick for any parallelogram:

_____________
|  /      .  /
| /       . /   <-- cut this part off, and move it ___
|/_________/                                          |
|
^                                                     |
|_________________ here ______________________________|

So the area of any parallelogram is the same as the area of the
rectangle with the same base and height. But the area of a rectangle
is just the base times the height - so that means

area(triangle) = (1/2) * area(parallelogram)

= (1/2) * area(rectangle)

= (1/2) * base * height

more, or if you have any other questions.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 06/29/2001 at 19:24:40
From: Christy V.
Subject: Re: math/area

Thank you, Doctor Math!
```
Associated Topics:
Elementary Geometry
Elementary Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons

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