jakolik wrote:
Hi,
The area of an equilateral triangle is \(9\sqrt{3}\). What is the area of it circumcircle.
A.10PI
B.12PI
C.14PI
D.16PI
E.18PI
Is this a GMAT question?
regards,
Jack
Edited the stem: it should be "The area of an equilateral triangle is \(9\sqrt{3}\)", (otherwise answer would be \({4\sqrt{3}\pi}\), which is not listed).
The area of an equilateral triangle equals to \(A=a^2\frac{\sqrt{3}}{4}=9\sqrt{3}\), where \(a\) is a side of a triangle --> \(a=6\).
The radius of the circumscribed circle for equilateral triangle is \(R=a\frac{\sqrt{3}}{3}=2\sqrt{3}\).
Area of a circle is \(\pi{R^2}=12\pi\).
Answer: B.
Or if you don't remember the formula for radius you should recall another property: radius of a circumscribed circle is 2/3 of the median, which for equilateral triangle is hight too. So calculate height from side and get the radius from it.
For more on this issue please check Triangles Chapter of the Math Book (link in my signature).
_________________
New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!
Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.
Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics