Question

What is the side of a regular polygon of $6$ sides inscribed in a circle with a radius of $15$ in?

Answer 1

Hint: In this problem we need to find the side length of the regular polygon with the given number of sides inscribed in a circle with the given radius. We know that the regular polygon means all the side lengths of the polygon are the same or equal. So, we will construct a regular polygon with $6$ sides in a circle of radius $15$ inches. Now we will join all the vertices of the polygon with the center of the circle. Now we can observe the formation of equilateral triangles having side length equal to the radius of the circle. From this we can calculate the required value.

Complete step-by-step answer:
Given that a regular polygon of $6$ sides inscribed in a circle with a radius of $15$ in.
Let us first construct a circle with radius $15$ in. The diagram of the circle will be

We know that the regular polygon means the polygon with equal side lengths. So, we are going to construct a regular polygon with $6$ sides in the above circle then we will get

Now joining all the vertices of the polygon with center of the circle then the diagram will be

We can observe that in the above diagram we can observe that equilateral triangles of having side length equal to the radius of the circle.

Hence the side length of the polygon is $15$ inches.

Note: In this problem we have to construct the regular polygon inside a circle because they have mentioned that polygon is inscribed in the circle. If they have mentioned that the polygon is described in the polygon, then we need to construct the polygon outside the circle as shown below