The correct option will be option C: The radius c will be 12.36 cm.
What is the radius of a regular pentagon?
The radius of a regular pentagon is the distance between the center of pentagon and the vertices of the pentagon.
A regular pentagon is given in the picture.
The sum of the angle of the regular pentagon is 540°
so each angle of regular pentagon will be =540°/5=108°
∠B=108°
Here the radius of the pentagon is OB.
Let the length of radius OB= c
The apothem OC divides the side of the pentagon in two equal parts.
where the length of the apothem OC =10 cm
The radius OB divides angle ∠B into 2 equal parts.
∠OBC=∅=∠B/2=108°/2=54°
in the triangle ΔOBC,
∠OCB=90°,
So the ΔOBC is a right-angled triangle.
then applying trigonometric properties
sin ∅ = OC/OB
⇒sin 54°=10/OB
⇒ sin 54°=10/c
⇒c=10/sin 54°
⇒c=12.36 cm
Therefore the radius c will be 12.36 cm.
Learn more about the radius of the pentagon
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