Asked by max

What is the area of a regular 30-gon with a radius of 9mm?

So far I know my interior angle is 6. That is all I can seem to figure out. Thanks!
Answered by Steve
The polygon is divided into 30 isosceles triangles, with vertex angle 360/30 = 12°

So, now you have 60 right triangles with one angle 6° and hypotenuse 9mm

So, the base of each triangle is 9sin6°, and the height is 9cos6°.

The total area is thus 60 * (1/2)(9sin6°)(9cos6°)

take a google at area of regular polygons to see how this relates to the formula

area = pa

where p is the perimeter and a is the apothem.
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