Question

A regular hexagon is inscribed inside a circle. the perimeter of the hexagon is 90 units.

a.what is the approximate measure of the radius of the circle?
b.what is the approximate area of the circle?

Answer 1

a The center of the hexagon and of the circle are the same point. Also length of one side of the hexagon = 90/6 = 15 units.

If we join each vertex of the hexagon to the center then we get 6 equilateral triangles (because internal angle of reg hexagon = 120 and vertex angles of the triangles = 60) so the radius = length of side of hexagon = 15 units (answer)

b Area = pi * 15^2 = 706.9 units^2 to nearest tenth. Answer