Find the area of the regular 20​-gon with radius 13 mm.

1 Answer

  • Inside a circle with a radius of 2mm, a 20-sided regular polygon is inscribed.
    Each of the 20 vertices is on the circuference of the circle, at 2 mm from the center.
    Since the polygon is a regular 20-gon, all the sides an angles have the same measure, and you could connect all the vertices to the center and split that 20-gon into 20 isosceles triangles with 2mm legs.

    As we are splitting, let's draw a line from the middle of each side to the center, spiltting each isosceles triangle into 2 right triangles.

    The area of the 20-gon, made up of 40 of those little right triangles, will be 12.36mm^2