Question

Consider an n-sided regular polygon inscribed in a circle of radius r. Join the vertices of the polygon to the center of the circle, forming n congruent triangles. Determine the central angle theta in terms of n. Show that the area of each triangle is (1/2)r^2sintheta. Find the limit of the area as n approaches infinity.

Answer 1

a. Theta = 360/n ( angles around a point)

Explanation:

n =Number of congruent triangles ( angles having the same angles and. Sides but not in the same direction).

This develops the assumption that each of the triangles created are equal and sides are equal.

Area of ∆ is given by 1/2 * b* h

Since all triangles are congruent b =h As they are all radius size

Area = 1/2 * (r *sin(theta)) * (r)

Area = 1/2*r^2sin(theta).

As n increases r *sin(theta) tends to 0