Question

if a hexagon is inscribed in a circle of radius r so what will be the perimeter of hexagon?

Answer 1

let the heagon be ABCDEF and O be the centre of te circle.

see. in a regular hexagon all the sides are equal. so the angle formed at centre by joining the vertexs of the hexagon with the centre is equal to

theta = 360/6 = 60o.

thus. if we consider any 1 triangle. let it be

ABO. then OA = OB =r.

also, angle, AOB = 60o

thus, by angle sum property we get

angle OAB = OBA = AOB = 60.

this implies that AOB is an equilateral triangle. so,

AB = r cm.

thus, side of hexagon = r

perimeter = 6r.