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:

The correct option is;

20-gon

Step-by-step explanation:

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

[tex]A = \dfrac{n \times s \times a}{2} = \dfrac{P_p \times a}{2}[/tex]

Where;

n = The number of sides

s = The length of one side of the polygon

a = The apothem

[tex]P_p[/tex] = The perimeter of the polygon

Where

The area of a circle, A[tex]_c[/tex] = 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.

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Short Answer
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Help plss!!!
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