How to Decompose Polygons

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Decomposing polygons allows you to work with simpler, more fundamental shapes. Decompose polygons with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Trigonometry, Graphs, & Other Math Tips
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Video Transcript

Hello, my name is Walter Unglaub, and this is how to decompose polygons. So, polygons, like this trapezoid I've drawn here, can be decomposed in to various simpler, more fundamental shapes. So here, what I want to look for are sections of my polygon where I can split it up into rectangles and triangles for example. So here I've drawn this line which is at a, which is at a 90 degree angle to the base, so I'm going to have two areas here, area one and area two, and now you see that the trapezoid is composed of simpler shapes. So, if I wanted to calculate the area of the trapezoid, I could calculate the area of the rectangle, for example, which would be six times nine, which is equal to 54, and the area of the triangle, which is going to be equal to one-half the base times the height. The base is going to be equal to this longer side minus the shorter side, so 12 minus 9, and my height of course is six, so the six turns into a three when I divide it by two, so I have three times three, which is equal to nine. So finally, the entire area of my polygon is going to be equal to 54 plus 9 which is equal to 63. I was able to easily and quickly find the area of this trapezoid of this polygon by decomposing it into simpler geometrical structures. And by finding the areas of each of those shapes you simply add up the areas and you get the total area of your polygon. My name is Walter Unglaub, and this is how to decompose polygons.

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