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  • 01-02-2020
  • Mathematics
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Approximate the area of a circle of radius 3 using a circumscribed regular hexagon.What is the percent error IN TERMS OF PI of the approximation?

Approximate the area of a circle of radius 3 using a circumscribed regular hexagonWhat is the percent error IN TERMS OF PI of the approximation class=

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MathPhys
MathPhys MathPhys
  • 02-02-2020

Step-by-step explanation:

The hexagon can be divided into six equilateral triangles.  The height of each triangle is 3, so using 30-60-90 triangle properties, the base is 2√3.

That means the area of each triangle is:

A = ½ (2√3) (3)

A = 3√3

So the area of the hexagon is 6A = 18√3.

The percent error is:

(18√3 − 9π) / 9π × 100%

(2√3/π − 1) × 100%

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