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 Does this help? Write back if you'd like to talk about this some 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!
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