So all of them,īy side-side-side, they are all congruent. This third common side of 2 square roots of 3. Side and this side be congruent to each otherīecause G is in the center. If we go all the way around the circle like that, Is equal to that length, which is equal to that length, Is equal to that length, which is equal to that length, which G which we can call the center of this polygon. Which is the same thing as GA, which is the same thing as GF, So that GD is the same thing as GC is the same thing as GB, It's equidistant from all of the vertices, And when I'm talking aboutĪ center of a hexagon, I'm talking about a point. And let's say it's the center of the hexagon. Videos, we'll think about the more generalĬase of any polygon. They want us to find theĪrea of this hexagon. This side over here isĪround the hexagon. And since this isĪ regular hexagon, they're actually giving us Sides, have the same length and all of the interiorĪngles have the same measure. Part lets us know that all of the sides, all six And this regular part-ĭealing with six sides. If these were not equilateral you would have to use the apothem and the Pythagorean theorem. And since we know the radii that means the remaining side is the sme measure at 8 cm. So this shows al four angles are 60 degrees, which means not only is it a scalene triangle, but an equilateral triangle. One angle is 60 and the other two are some other angle x where all three equal 180. so in other words use some algebra to find the two other angles. Also, you should know the angles of a triangle add up to 180. Since it is a scalene triangle you know the measure of the other two angles are the same. this means each triangle will have an angle of measure 360/n, where n is the number of sides. Basically each side will have one of these. You want to count how many of these triangles you can make. You know both radii are 8 cm, which means you have an isosceles triangle. it is also important to know the apothem This works for any regular polygon.Ĭhoose a side and form a triangle with the two radii that are at either corner of said side. Radius is the distance from the center to a corner.
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