SOLUTION: 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)https://media.glynlyon.com/

Question 763263: 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)https://media.glynlyon.com/g_geo_2012/8/groupi56.gif
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

you need to use the area of "Sector of the circle" formula

where n is the number of degrees in the central angle of the sector
your shaded area is equal to area of the triangle minus area of three sectors of the circle
area of the triangle:
sides length: ,,
find height which divides triangle into two right angle triangles whose sides are: hypotenuse , one leg is and other leg is
so,

now we can find the area of triangle :

now find area of circle sector:
........,

you have three of these sectors, so total area is

now we can find the area of the shaded portion: it is equal to difference between the area of the triangle and three sectors

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