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=](https://us-static.z-dn.net/files/dd3/3f5d8d10787603bed8cd121b2287e467.jpg)
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%