Finding the Area of a Regular Polygon

[Lou Lou]

I need help finding the area of a regular hexagon. We have gone over this topic, but it has been a while and now it is coming back to haunt me with finding the volume of 3D prisms.

So I have a regular hexagon, the sides and angles are all equivalent, the sides are 6 m. I know that the angles are 720 deg. But, if i want to find the area of the hexagon, don't I have to make a special right triangle, to get the height and then plug it into the formula to find the volume?

~*~Any help is appreciated. Thank you so much!!!~*~

 

[stapel]

There's probably a formula for this, but, yes, you can make right triangles and work from there.

From the center, draw lines to a vertex and to the midpoint of a side that terminates at that vertex. Since the sides are all congruent, the midpoint line is a perpendicular bisector, so you now have a right triangle. From the given side-length value, you know that the "base" of the triangle (the half of the outer edge) has length 3.

You can form ten such triangles. Since their at-the-center angle measures have to add up to 360° (for a full circle), you can then find the angle measure for that at-the-center angle formed by the two lines you drew from the center.

With one side length and an angle measure, you can find the length of the bisector. This is also the "height" of the triangle. With the height and base, you can find the area.

Then multiply by "10".

Eliz.