Regular Polygon: when a shape has equal interior angle and equal side lengths, it is called a regular polygon.
Mr. Backe, then drew a picture that was identified as a five sided regular polygon. The diagram below shows that the two polygons are similar (~). The ratio for each side of the pentagon will have a ratio of 4:8 or 8:4 if the measurements were 4 and 8.
The next shape we were worked with was similar to the shapes in the diagram above although it is connected and some angles are not the same as the one above. The shape looked something like this:
First we put the down the ratios of the corresponding angles and sides which will eventually help solve our problem.
There were two methods we did to find the missing side lengths. The first method was to divide the only corresponding sides that have measurements for both small and big polygon and use that as a scale factor. In this case the ratio is 2/5 and when you divide 2 and 5 you get 0.4 which will then be your scale factor. You then use that scale factor to find the other missing side lengths by multiplying their corresponding side by 0.4. This goes for all of them.
The second method we did was to use a proportional expression to solve the missing side lengths. We used the variable x to represent the missing side lenghts. All the work is shown in the diagram above.
- use the provided diagram above to find the perimeter of the small polygon.
- 4.4 Practise: 3,5,6
- 4.4 Apply: All
- 4.4 Extend: 13-17
*NOTE: click the picture for a larger view.