find the area of a regular decagon with radius 6 cm

Question

find the area of a regular decagon with radius 6 cm (pls help)

Answer 1

A decagon is made up of 10 congruent triangles. Find the area of one triangle and multiply by 10.

Imagine the decagon in a circle of 360 degrees, then the central angle of each triangle is 360/10 = 36.

The two sides that include that angle are the radii of 6 cm.

The area of a triangle with two sides a, b and an included angle C is 1/2 a b sin (C).

Here a = b = 6 and C = 36.

Compute the area of the triangle using that formula then multiply by 10 to get the entire area of the decagon.