Consider an -sided regular polygon.

The radius of circle is .

The number of triangles are .

(a)

Find the central angle in terms of .

The total angle in a circle is .

The central angle is divided into parts.

The angle .

(b)

Show that the area of each triangle is .

The radius of circle is the height of the triangle.

In a triangle

.

The area of the triangle is .

.

The area of the each triangle is .

(c) Find .

Let be the sum of the areas of the triangles.

As , then .

Apply formula .

.

.

(a) The angle .

(b) The area of the each triangle is .

(c) .