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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(1/2sh)



Which statement is true?

A. - As h increases, ns gets closer to 2πr​.

B. - As s increases, ns gets closer to 2πr​.

C. - As r increases, ns gets closer to 2πr

D. - As n increases, ns gets closer to 2πr​.

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 t class=

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Catya
D. as n increases, ns --> 2πr
 h/r cannot increase it is the circle radius
s, side length we want to get smaller and smaller to make a circle

aksnkj

The polygon will become a circle when the value of ns becomes equal to circumference or

[tex]2\pi \: r[/tex]

It is required to make a polygon into a circle.

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.

Now, the area of the polygon is given to be polygon area = n(1/2sh).

Now, to get a circle, we need to assume that the sides of the polygon is infinite. And to do so, we need to assume that the perimeter of the polygon is equal to the perimeter of the circle.

The perimeter of the polygon can be written as

[tex]ns =2 \pi \:r[/tex]

Therefore, the polygon will become a circle when the value of ns becomes equal to circumference or 2

[tex]\pi[/tex]

r.

for more details, refer to the link:

https://brainly.com/question/19467889

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