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An equilateral triangle that has an area of 9*root(3) [#permalink]
 25 Nov 2010, 02:11
Question Stats:
67% (02:09) correct
32% (01:07) wrong based on 46 sessions
An equilateral triangle that has an area of 9\sqrt{3} is inscribed in a circle. What is the area of the circle? A. 6pi B. 9pi C. 12pi D. 9pi 3^1/2 E. 18pi 3^1/2 This is how I solved it area of equilateral triangle =Square root 3/4*a^2=9 square root 3 we get a =6 know to calculate radius of an equlateral triangle in an inscribed circle we can use formulae r=a*square root 3/6 with this I get r=square root 3 and then area =3 pi  but its not in the answer choices OA is something else ....
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Re: Equilateral triangle question [#permalink]
25 Nov 2010, 02:30
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rite2deepti wrote: An equilateral triangle that has an area of 9 3[/square_root]1/2 is inscribed in a circle. What is the area of the circle? A . 6pi B. 9pi C. 12 pi D. 9pi 3^1/2 E. 18pi 3^1/2 This is how I solved it area of equilateral triangle =Square root 3/4*a^2=9 square root 3 we get a =6 know to calculate radius of an equlateral triangle in an inscribed circle we can use formulae r=a*square root 3/6 with this I get r=square root 3 and then area =3 pi but its not in the answer choices OA is something else .... I'd recommend to know the ways some basic formulas can be derived in geometry rather than memorizing them. Anyway, area_{equilateral}=a^2*\frac{\sqrt{3}}{4}, where a is the length of a side --> as given that area_{equilateral}=a^2*\frac{\sqrt{3}}{4}=9\sqrt{3} then a=6; Now, given that this triangle is inscribed in circle (not circle is inscribed in triangle). The radius of the circumscribed circle is R=a*\frac{\sqrt{3}}{3}=2\sqrt{3} (you used the formula for the radius of the inscribed circle r=a*\frac{\sqrt{3}}{6}) --> area_{circle}=\pi{R^2}=12\pi. Answer: C. Check Triangles chapter of Math Book for more: math-triangles-87197.htmlHope it helps.
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Re: Equilateral triangle question [#permalink]
27 Nov 2010, 18:50
Use the formula to calculate area of the inscribed circle to the equliateral triangle. Bunuel's guide on Triangles has all the important formulae in it..
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An equilateral triangle that has an area [#permalink]
15 May 2012, 20:53
An equilateral triangle that has an area of 9 root 3 inscribed in a circle. What is the area of the circle? 1. 6Pi 2. 9 Pi 3. 12Pi 4. 9Pi*3^1/2 5. 18Pi*3^1/2
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Re: An equilateral triangle that has an area [#permalink]
15 May 2012, 21:07
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monir6000 wrote: An equilateral triangle that has an area of 9 root 3 inscribed in a circle. What is the area of the circle?
1. 6Pi
2. 9 Pi
3. 12Pi
4. 9Pi*3^1/2
5. 18Pi*3^1/2 Hi Moneer First determine the side of Eq triangle by formula area of eq T= (Sqrt3/4)* (side)^2 This gives side of eq T= 6 Also The radius of the circumscribed circle is R= (Sqrt3/3)*(Side) So R= 2 Sqrt 3 Area of circle= Pie*R^2 = 12 Pie Hope this clrifies Best Vaibhav
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Re: An equilateral triangle that has an area [#permalink]
15 May 2012, 21:15
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monir6000 wrote: An equilateral triangle that has an area of 9 root 3 inscribed in a circle. What is the area of the circle?
1. 6Pi
2. 9 Pi
3. 12Pi
4. 9Pi*3^1/2
5. 18Pi*3^1/2 Hi Monir First determine the side of Eq triangle by formula area of eq T= (Sqrt3/4)* (side)^2 This gives side of eq T= 6 Also The radius of the circumscribed circle is R= (Sqrt3/3)*(Side) So R= 2 Sqrt 3 Area of circle= Pie*R^2 = 12 Pie Hope this clrifies Best Vaibhav
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Re: An equilateral triangle that has an area [#permalink]
15 May 2012, 21:28
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Area of the triangle = a^3/4R where a is a side of the triangle and R is the radius of the circle sqrt(3)(side^2)/4 = 9*sqrt(3) => side = a = 6 9*sqrt(3) = 216/4R => R = 6/sqrt(3) So area of the circle = pi*36/3 = 12pi Option 3
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Re: An equilateral triangle that has an area [#permalink]
15 May 2012, 23:56
Now this math is clear to me. thanks everyone.
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Equilateral Triangle in Circle, Find Area of Circle [#permalink]
01 Oct 2012, 14:00
An equilateral triangle that has an area of 9\sqrt{3} is inscribed in a circle. What is the area of the circle?
A. 6 PI
B. 9 PI
C. 12 PI
D. 9PI\sqrt{3}
E. 18PI\sqrt{3}
How does one do this?
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Re: Equilateral Triangle in Circle, Find Area of Circle [#permalink]
02 Oct 2012, 00:30
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Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
18 Dec 2012, 04:32
Formula
Triangle inscribed in a circle.
area of the triangle inscribed in a circle with radius "r" = (abc)/4r
a,b,c - are the sides of a triangle inscribed
r - is the radius of the circle.
Circle inscribed in a Triangle
are of the triangle = (a+b+c)r/2
a,b,c - sides of a triangle
r - radius.
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Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
13 May 2013, 00:03
rite2deepti wrote: An equilateral triangle that has an area of 9\sqrt{3} is inscribed in a circle. What is the area of the circle? A. 6pi B. 9pi C. 12pi D. 9pi 3^1/2 E. 18pi 3^1/2 This is how I solved it area of equilateral triangle =Square root 3/4*a^2=9 square root 3 we get a =6 know to calculate radius of an equlateral triangle in an inscribed circle we can use formulae r=a*square root 3/6 with this I get r=square root 3 and then area =3 pi but its not in the answer choices OA is something else .... the above calculation is correct. since 9pi3^1/2= 9pi/3=3pi so the correct answer is D.
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Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
13 May 2013, 01:27
rite2deepti wrote: An equilateral triangle that has an area of 9\sqrt{3} is inscribed in a circle. What is the area of the circle?
A. 6pi
B. 9pi
C. 12pi
D. 9pi 3^1/2
E. 18pi 3^1/2
using the area of the triangle we can get the side of the equilateral triangle using area = (\sqrt{3}/4) x a^2 We can get the side as 6. now we have the sine formula for the triangle. ie a/sinA = 2R. where R the circumradius of the triangle. a is the side and A is the corresponding angle. We have A = 60 a = 6 we can get R.which will be 2\sqrt{3}. So the area of the circle will be 12 pi
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Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
13 May 2013, 01:28
khosru wrote: rite2deepti wrote: An equilateral triangle that has an area of 9\sqrt{3} is inscribed in a circle. What is the area of the circle? A. 6pi B. 9pi C. 12pi D. 9pi 3^1/2 E. 18pi 3^1/2 This is how I solved it area of equilateral triangle =Square root 3/4*a^2=9 square root 3 we get a =6 know to calculate radius of an equlateral triangle in an inscribed circle we can use formulae r=a*square root 3/6 with this I get r=square root 3 and then area =3 pi but its not in the answer choices OA is something else .... the above calculation is correct. since 9pi3^1/2= 9pi/3=3pi so the correct answer is D. The correct answer cannot be D...the answer must be C... from the formula of area of triangle you can calculate the side of triangle ie 6. Now the radius of circumcircle (for equilateral triangle) is side/root(3) So substitute to get the final answer ie C Consider kudos if my post helps!!!!!!!!!!!!!1 Archit
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Re: An equilateral triangle that has an area of 9*root(3)
[#permalink]
13 May 2013, 01:28
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