Question

Select the correct answer. The area of a polygon of n sides inscribed in a circle of radius r is . If r = 12, what is the limit of A as n approaches infinity? A. 452.39 B. 658.02 C. 37.70 D. 226.19

Answer 1

452.39

Explanation:

PLATO right? I did the test

Answer 2

The correct option is;

A. 452.39

Explanation:

Here we are required to find the area of a polygon which is inscribed in a circle.

The radius, r of the circle = 12

The number of sides of the polygon = n

The area is required as n approaches infinity

We note that as the number of sides of the polygon increases, the perimeter of the polygon increasingly approximates the perimeter of the circle.

Therefore, as the number of sides approaches infinity, the area of the polygon is approximately the area of the circle.

The area of the circle is therefore found as follows;

The area of a circle = π·r² = π × 12² = 452.39 unit²

Therefore, as n → ∞, the area of the polygon = 452.39.