May 9 2013
Hello Timmy! I heard you have been sick with the flu for a while so, I took the liberty of getting you on your feet before class so you are not lost. So this paper will help you find the area of a hexagon using special right triangles, using trigonometry, breaking the hexagon into smaller polygons, and even show you how to construct one! So let’s get started, this hexagon has a radius of 6 cm, keep in mind that there are many different ways to do find the area of a hexagon. Use the formula 1/2asn meaning; ½ (apothem) (side length) (number of sides).You can put two radii (radii is a term for more than one radius) together and make a triangle. There is a problem we do not know the apothem (line segment of a regular polygon from the center to the midpoint of one of its sides)! In order to find the apothem you must find the angle measure of the central angle 360/the number of sides so it would be 360/6 which is 60.Then draw a line down the middle of the triangle, then you must cut it in half so, 60/2= 30 at this point you realize that the two triangles are 30-60-90 triangles. Since you know the hypotenuses is four you divide six by two, and stick a radical three on the end of it and, viola! You have your apothem. You may have noticed that the triangle that makes the hexagon is equilateral which means that the base of the triangle is also six. This is great we know all of the pieces to the formula. ½ (3√3)(6)(6 ( hexagons always have six sides, just saying!)) =54√3 cm.
You are doing great Timmy, now you should know that you can’t always use special right triangles to find the apothem you must use trigonometry to find the apothem. The apothem bisects the equilateral triangle ( all triangles in a hexagon are equilateral) into two 30-60-90 triangles, the...