Find the area of a regular 36-sided polygon inscribed in a circle of radius 20

Answer 1

360/36 = 10 degrees center angle for each of the 36 isosceles triangles with equal sides of length 10
10 cos 5 degrees = h
sin 5 = (b/2)/ 10 so b/2 = 10 sin 5
A of each of the 36 = h b/2 = 10 cos 5 * 10 sin 5 = 100 sin 5 cos 5
A = 36 * 100 sin 5 cos 5 = 314
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check, should be a touch less than circle area
pi r^2 = 100 * 3.14159
LOL close enough

Answer 2

the apothem is 20 cos5° = 19.923
the side length is 2*20sin5° = 3.486
the area is 1/2 * perimeter * apothem = 1250.1

area of a circle of radius 20 = 400π = 1256.6