# The segment of a polygon

THE SEGMENT OF A POLYGON

By: Risa Santoso 11DP-2

The purpose of this investigation is to find the relationship of the ratios of sides and the ratios of area in a polygon. By doing this investigation, we will be able to acquire more skills and knowledge about shapes and the relationship between the lines of sides and area of a shape with the help of trigonometry.

To find the relationship of the ratio of sides and area in a polygon, we use the “Geometer’s Sketchpad” program.

Table of result

From the table above, we can spot clearly that the more ‘n’ (from 1:n) in the ratio, the more length increases in the sides and the area of the inner (the small) triangle. However, the ratio between the area of the outer and the inner triangle’s gap became smaller (1:7 (inner: outer) can be written as 1: 0.143, 4: 13; 1: 0.308 and 3: 7; 0.429). This shows that the area of the inner triangle increases when the ratio sides increases while the outer triangle stays the same. There is also a pattern shown in the ratio of the ...