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?
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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%