Question

A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle.

Let s be the side length of the polygon,


let r be the hypotenuse of the right triangle,


let h be the height of the triangle, and


let n be the number of sides of the regular polygon.




polygon area = n(12sh)





Which statement is true?



As r increases, the area of the regular polygon approaches the area of the circle.


As n increases, the area of the regular polygon approaches the area of the circle.


As s increases, the area of the regular polygon approaches the area of the circle.


As h increases, the area of the regular polygon approaches the area of the circle.

Answer 1

as n increases, the area of the regular polygon approaches the area of the circle I believe

Answer 2

As n increases, the area of the regular polygon approaches the area of the circle.

Explanation:

A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle.

The polygon area can be expressed in terms of the area of a triangle.

Let s denote the side length of triangle.

r hypotenuse of right triangle.

h height of the triangle.

let n be the number of sides of the regular polygon.

The area of polygon is given by:

polygon area = n(12sh)

The correct statement is:

As n increases, the area of the regular polygon approaches the area of the circle.

" Since, as the number of sides of the polygon increases the polygon start approaching to the circumference of circle and as n tends to infinity the polygon will tend to take the shape of the circle "