GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 28Live Online Class with Top GRE Expert Mike Butville
08:00 PM EDT
-10:00 PM EDT
Top scores are possible when you enroll in a powerful GRE course, taught live online + 6 months access to TTP GRE OnDemand video courses included! Class starts Mon/Wed Sept. 28, 2026 - Dec. 9, 2026, 8:00pm-10:00pm EST
If the circle with center O has area 9π, what is the area of
[#permalink]
11 Dec 2018, 13:34
11 Dec 2018, 13:34
Expert Reply
3
Bookmarks
00:00
Question Stats:
72% (02:23) correct
27% (02:17) wrong based on 83 sessions
Hide Show timer Statistics
If the circle with center O has area 9π, what is the area of equilateral triangle ABC?
#GREpracticequestion If the circle with center O has area 9π, what is the area of equilateral triangle ABC.jpg [ 11.68 KiB | Viewed 14577 times ]
A. \(9 \sqrt{3}\)
B. \(18\)
C. \(12 \sqrt{3}\)
D. \(24\)
E. \(16 \sqrt{3}\)
Attachment:
#GREpracticequestion If the circle with center O has area 9π, what is the area of equilateral triangle ABC.jpg [ 11.68 KiB | Viewed 14577 times ]
A. \(9 \sqrt{3}\)
B. \(18\)
C. \(12 \sqrt{3}\)
D. \(24\)
E. \(16 \sqrt{3}\)
Re: If the circle with center O has area 9π, what is the area of
[#permalink]
17 Dec 2018, 21:06
17 Dec 2018, 21:06
1
Expert Reply
1
Bookmarks
the clue here is that we have an equilateral triangle, which means each triangle is a 30,60,90 triangle.
keep that in mind.
the area of the circle is 9pi, which means the radius is 3 and the diameter of the circle is 6.
this diameter is the height of your triangle, now we need to find the base of it. It's already split in two for us, so no need to use 1/2bh for the area, just use bh
since it's a 30, 60, 90 triangle, just divide the height by sqrt(3)
The answer is C
so h =6/Sqrt(3)
then B*H=6/sqrt(3)*6=36/sqrt(3)= 12sqrt(3)
keep that in mind.
the area of the circle is 9pi, which means the radius is 3 and the diameter of the circle is 6.
this diameter is the height of your triangle, now we need to find the base of it. It's already split in two for us, so no need to use 1/2bh for the area, just use bh
since it's a 30, 60, 90 triangle, just divide the height by sqrt(3)
The answer is C
so h =6/Sqrt(3)
then B*H=6/sqrt(3)*6=36/sqrt(3)= 12sqrt(3)
Re: If the circle with center O has area 9π, what is the area of
[#permalink]
12 Oct 2021, 21:21
12 Oct 2021, 21:21
2
This is an equilateral triangle, three sides of equal length is a and three equal 60 degrees angles.
Given that the area of the circle is 9π,
we know area of circle is πr^2=9π
so, r=3
Diameter AD=2r=6,
Now AD=h of triangle=6
we know The height h of an equilateral triangle is
h=a sin60 =6
=>a sqrt(3)/2 =6
=>base a=12/sqrt(3)
area is: 1/2*a*h =1/2*12/sqrt(3) * 6
=(12*3)/sqrt(3)
=12 sqrt(3)
Given that the area of the circle is 9π,
we know area of circle is πr^2=9π
so, r=3
Diameter AD=2r=6,
Now AD=h of triangle=6
we know The height h of an equilateral triangle is
h=a sin60 =6
=>a sqrt(3)/2 =6
=>base a=12/sqrt(3)
area is: 1/2*a*h =1/2*12/sqrt(3) * 6
=(12*3)/sqrt(3)
=12 sqrt(3)
