Does the area of the polygon continue to increase as the number of sides increase?

Does the area of the polygon continue to increase as the number of sides increase?

As the number of sides keeps increasing, the area of the circle enclosed in the regular polygon keeps increasing till the number of sides is infinite (i.e. we get a circle) and it overlaps with the original circle.

What is the relationship between a circle and a regular polygon?

That is, a regular polygon is a cyclic polygon. Together with the property of equal-length sides, this implies that every regular polygon also has an inscribed circle or incircle that is tangent to every side at the midpoint. Thus a regular polygon is a tangential polygon.

What happens to the inscribed polygon as the number of it’s sides increases?

As the number of sides increases, the apothem gets closer and closer to the radius of the circle. As the apothem approaches 1, the perimeter of the polygon approaches 2π, the circumference of the circle.]

What do you call a polygon that is both equilateral and equiangular?

Regular Polygons Equilateral polygons have congruent sides, like a rhombus. Equiangular polygons have congruent interior angles, like a rectangle. When a polygon is both equilateral and equiangular, it is called a regular polygon. A square is an example of a regular polygon.

Which is greater a circle or a polygon?

But we know that that value is greater than or equal to the circumference of the circle (because it’s the perimeter of the larger polygon) and also less than or equal to to the circumference of the circle (because it’s the perimeter of the smaller polygon).

Can a polygon be both less than and equal?

There’s only one way that it can be both less than or equal and greater than or equal, and that’s if it’s equal. So, in the limit as the number of sides goes to infinity, the polygon IS the circle.

Can a polygon have an infinite number of sides?

You can have polygons with sides for arbitrary large. So can be , or or whatever integer you want. But I don’t see how you can ever get a polygon with an infinite number of sides. If you say “increase the number of sides” then that’s clear.

What happens when an object comes closer to a convex lens?

Copy If the object is at infinity, the image is formed at the focus and is:- 1)real 2)inverted 3)highly diminished If it is a bit beyond the center of curvature(C), it is formed a bit beyond focus(F) and is:-