What is the formula of an apothem?

Answer 1

The apothem of a regular polygon? well lets look at the math behind it before i recall it... you can scroll down to the bottom of the page if you don't want to read this. the formula is on the bottom of the page * A regular polygon is made up of a sequence of isoceles triangles.. * How do we know that they are isoceles? ------1)the triangles that make up a regular polygon are congruent -------2)the radii are always congruent . the radii of a regular polygon goes from it's center to the vertices...(hint:think of a circle's radius) * due to the fact that you have isoceles triangles they have to be made by angle bisectors through the regular polygon otherwise they couldn't be congruent * okay now that we know that the triangles are isoceles we also know that the apothem is an angle bisector so it cuts the measurement of a side in half. lets use j for our the measurement of our side. * okay we got the angle measures and our apothem made two congruent triangles so now we can use trig ratios to find our apothem so the formula is a=0.5j(tan [n-2]*180/2n) where n is the # of sides and j is the measurement of a side or you can simplify that to a=0.5j(tan [n-2]*90/n) i am using degrees for my angle meausure by the way