Question

Find the area of the shaded portion in the equilateral triangle with sides 6.
(assuming the central point of each arc is its corresponding vertex)

Answer 1

ok you need to do the following:
1) find the area of the triangle. notice that the triangle is equilateral thus we can use this:\[Area= \frac{ 1 }{ 2 }*\sin60* 6^{2}\]
2) find the area of the of the three equal sectors , and it equals one third of the area of circle it's radius=3 ,and it's given with the following formula:\[Area=\frac{ 1 }{ 3 }*\pi *3^{2}\]
so now the area = \[9\sqrt{3}-3\pi\]
that's what I think..

Answer 2

I thought 3 had to be divide by something beacause that's what my answer has to be like this something sqr- something divide by something pi

Answer 3

lol even I did not understand much, but I can tell you that devision has nothing to do with evaluating any non-regular areas in such questions like yours, always think about this :\[Area= Area1 -Area2\]

Answer 4

my answer has to be it that format tho

Answer 5

each sector has a central angle of 60º and radius of 3
the area of one sector is (60/360) * pi * 3^2= 9/6 pi or 3/2 pi

there are 3 congruent sectors, with a total area of 9/2 pi