650 + questions geometry

[freezer]

The area of an equilateral triangle is 9.what is the area of it circumcircle.
A.10π
B.12π
C.14π
D.16π
E.18π



Could anybody give me a step by step solution?

Thanks

[ken_english]

is it 10 pi

[tublai]

"a" = length of a side of equilateral triangle

sqrt(3) / 4 * a^2 = 9 as per the question stem

=> a^2 = 12 * sqrt(3)

Radius of circumcricle of an equilateral triangle ( this is special case ) = a / sqrt(3)

=> R = a / sqrt(3)

=> R^2 = a^2 / 3 = 4 * sqrt(3)

Area of circumcircle = pi * R^2 = pi * 4 * sqrt(3)


I am not getting any of the above answer choices..Not sure where I am going wrong..

[notsofast]

Ken English can you explain your answer?

Tublai I don't get it at all. What does "a" mean? If "a" is area of the triangle we're given that.

I'm sorry but both of these are totally unhelpful.

[tublai]

Ken English can you explain your answer?

Tublai I don't get it at all. What does "a" mean? If "a" is area of the triangle we're given that.

I'm sorry but both of these are totally unhelpful.

I'm sorry notsofast..I forgot to mention what is "a"

a = side of equilateral triangle, then area of that equilateral triangle is sqrt(3) / 4 * a^2

I have edited my earlier post..

[Protagonist]

My answer is 4*rt3*pi

[Protagonist]

Here are some Equilateral Triangle properties :

For an Equilateral Triangle with side 'a':

Circumscribed Circle Radius

Inscribed Circle Radius

Area


Perimeter


Altitude


Median

[samdamn]

answer is 4 pi sqrt 3

[samdamn]

you can solve it even if you dont know the formulaes

lets assume radius is r; side is a; ht is h

we can form the equations to arrive at the solution...

let me see if I can draw something and attach it here

[Protagonist]

yes you are right, all the above formulae can be derived easily