Find the area of a regular decagon inscribed in a circle of radius 12cm?

Question

Please some genius help my younger sis with this difficult sum. I suck at math.

Thanks a bunch!

10points..

Answer 1

10 triangles
=> area = 10 * 1/2 ab sin C
=> area = 10 * 1/2(12)(12) sin 36........360/10
=> area = 10 * 42.320
=> area = 423.20 cm^2

QED

Answer 2

A decagon has 10 sides making 10 equivalent triangles such that each will have an interior angle (i.e. at the center of the circle) of 360/10 = 36 degs and two sides of 12cm each.

Each can be bisected to make a right triangle with minor angle 18 degs and hypotenuse = 12. Therefore, the opposite side from the 18 deg angle is 12sin18 = 3.7 and the adjacent side is 12cos18 = 11.4

Therefore the area of each bisection (20 of them) is 0.5*3.7*11.4 = 21.1.

Area of the decagon is 20* 21.1 = 422 cm^2

I would trust Harry's answer more than mine. Plus his solution is more direct. ;-)