We know that to find the area of the entire circle, we are going to use the equation:
[tex] A=\pi r^{2} [/tex]
And we know that the diameter is 12. To find the radius, we divide the diameter by 2, so 12/2 = 6. So the radius is 6.
Now we can use this radius in the equation:
[tex] A=\pi (6)^{2} [/tex]
[tex] A=36\pi [/tex]
Since all of the angles of each section are equal, we can assume that each of the sections has an equal area. There are 5 sections, so we need to divide [tex] 36 \pi [/tex] by 5 to find the area of each section:
[tex] \frac{36 \pi}{5} =7.2 \pi [/tex]
Each section has an area of [tex] 7.2\pi units^{2} [/tex] or, using 3.14 for pi, [tex] 7.2*3.14=22.61units^{2} [/tex].
Since we are told to find the area of the blue sections, we know that there are 2 sections that are blue. So we need to multiply the area of each section by 2, to find the area of two of the sections:
[tex] 22.61*2=45.22units^{2} [/tex]
Therefore, the answer is C) 45.2 [tex] units^{2} [/tex].
