Question

Which of the following regular polygons circumscribed about a circle provides the best estimate for the area of that circle?

dodecagon
decagon
20-gon
11-gon

Answer 1

The correct option is;

20-gon

Explanation:

The area, A, of a regular polygon is given as follows;

`A = (n * s * a)/(2) = (P_p * a)/(2)`

Where;

n = The number of sides

s = The length of one side of the polygon

a = The apothem

`P_p` = The perimeter of the polygon

Where

The area of a circle, A
`_c` = π×r² = π × r × r = 2× π × r × r/2 = P/2 × r

Given that the apothem, a, of a 20-gon circumscribed about a circle is approximately the length of the radius of the circle, and the perimeter of the 20-gon is approximately the perimeter (circumference) of the circle, the area of the 20-gon circumscribed about a circle provides the best estimate for the area of the circle.