Question

Express answer in exact form. Show all work for full credit.

Answer 1

Answer:

1.5 pi in.^2 - 2 & 1/4 sqrt 3 in.^2

Step-by-step explanation:

First, since the hexagon is a regular polygon, then each of the 6 equilateral triangles in the hexagon has all sides of 3 inches. This means that the radius of the circle is equal to 3 inches.  

To find the area of the circle: A = pi * r^2 --> A = 9 pi in.^2.

Next, find the area of the sector: 60o (o = degree sign) divided by 360o --> 60/360 = 1/6 --> 1/6 times area of circle (9 pi) =  

1.5 pi in.^2.

Then, find the area of one of the equilateral triangles by using the formula for the area of an equilateral triangle:  

A = 1/4 * s^2 * sqrt 3 --> A = 1/4 * 3^2 * sqrt 3 --> A = 2 & 1/4 sqrt 3.

Finally, to find the area of the segment, do the area of the sector minus the area of the triangle:  

1.5 pi in.^2 - 2 & 1/4 sqrt 3 in.^2 (this is the exact answer; for it to be an approximate answer, you would actually do the equation).

Hope this helps! :)

Answer 2

The chord length is the same as the radius, so R^2 = 9.
Area = (1/2)(9)(pi/3 - sqrt(3)/2) = (3/4) (2 pi - 3 sqrt(3))