By: Tim Lehman

Students will now combine what they have learned about area and the Pythagorean Theorem. They will find the area of different regular polygons.

The students first need to construct the regular
polygons on GSP. A hexagon is a good place to start. After constructing
the hexagon, its area should be found. First, we can see the hexagon
can be divided into six congruent triangles. The triangles are
also equilateral.** How do we
know they are equilateral?**

If the area of the triangles can be found, then the area of the hexagon will immediately follow. Because the triangles are equilateral, all of their sides are equal. Let's assume the length each side of the hexagon is 1 unit.

By using the Pythagorean Theorem, we can find
the height (in blue) of the triangle and, thus, the area of the
hexagon. **Click here** for
a GSP sketch of a hexagon.

Students with an understanding of trigonometry
can then go on to work on other polygons. For those who do not,
the students can be provided a trig table or be provided the lengths
needed. This would still leave the challenge of constructing the
polygons (**click here** for
an octogon with construction lines and **here**
for one without) and applying the theorem.