What geometric figure does a regular polygon begin to resemble as the number of sides increases?
A circle
Vhvv
As the number of sides in a regular polygon increases, it begins to resemble a circle.
A regular polygon is a polygon with all sides and angles equal. As the number of sides increases, a regular polygon begins to resemble a circle.
To understand why this happens, we can look at the formula for calculating the interior angle of a regular polygon:
Interior Angle = (n-2) * 180° / n
where n is the number of sides.
As the number of sides increases, the value of n becomes larger, making the interior angle of the polygon smaller. In the case of a circle, it has an infinite number of sides, therefore, the interior angle tends towards 0°.
When a regular polygon has a very large number of sides, the interior angles become very close to 0°, causing the polygon to appear more and more circular. This is why a regular polygon starts resembling a circle as the number of sides increases.