A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.
(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3.)
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maybe you can find the radius of the circle by looking at one of the triangles that make up the inscribed hexagon. That will allow you to get the whole circle area, and 1/6 of that area falls in the "pie piece" that includes the triangle.
Then, if you have the area of that triangle, subtract it from the pie piece to get the segment in question.
the radius of that circle will be 3. so are=pi r^2=28.27
by joining the centre with each corner of the hexagon u'll get the area of each part.
So Area of each part=28.27/6=4.545.............(i)
Area of the triangle= (3)^2*sq. root of 3/4=3.9.............(ii)
Now subtracting the area of equation (ii) from equation (i) u will get the result.
Area of circle with radius 3 = 3^2 pi = 9 pi. 1/6 of the circle = (9/6) pi = (3/2) pi
The triangle has hypotenuse 3, base 3, so the height is (3/2)sqrt(3).
The area of that triangle is (1/2)bh = (1/2)(3)(3/2)sqt(3) = (9/4)sqrt(3)
Area of 1/6 circle - Area of triangle = (3/2)pi - (9/4)sqrt(3)
= 4.712 - 3.897 = 0.815
That's what I got... but you need to double check the geometry and the math.
Ooops, i'm really sorry, JakeV8 is right. I've checked it right now. Actually, previously i made a calculation mistake..Sorry again..