The area of a circle and the area of a regular polygon of sides of the perimeter equal to that of that circle are in the ratio
Explanation for correct answer:
Step 1: Finding and
It is given that, the perimeter of a circle is equal to the perimeter of a polygon.
Let '‘ is the radius of a circle and ’' be the side of a regular polygon.
Therefore,
(’' is the number of sides of a polygon)
Let the area of a circle is denoted by ‘’
Therefore,
Let '' represent the area of a regular polygon, and the area of a polygon is calculated by using the formula given below.
Substituting the value of in equation we get,
Step 2: Determining the ratio of the two areas
By Dividing equation by equation we get,
Hence, option (A) is the correct answer.