How do you do this?
Show that the area of a regular polygon of n sides, each of length a is given by A=1/4n(a*a)cot(pi/n).
2007-11-07 12:24:31 · 1 answers · asked by Mia 2 in Science & Mathematics ➔ Mathematics
Draw all the line segments connecting the center to the vertices. Then you've divided it into n isocecles triangles, each of which has an apex angle of
... try to figure this out yourself for a moment ...
2 pi/n
Now drop the median to the base of each of those triangles. You'll have 2n right triangles, each of which has an angle of ...
... that's right ...
pi/n
And one of the sides of the triangle has length a/2. And you figure out the length of the other side by using trig.
And you surely know the formula for the area of a right triangle! :)
2007-11-07 19:27:59 · answer #1 · answered by Curt Monash 7 · 0⤊ 0⤋