Welcome! Check out our free B-School Guides to learn how you compare with other applicants.

## Geometry - Triangle Area

tagged by: lola27

This topic has 1 expert reply and 3 member replies
lola27 Just gettin' started!
Joined
22 Mar 2010
Posted:
3 messages
Geometry - Triangle Area Thu Jan 05, 2012 3:50 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateral triangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?

A. 169*sqrt3 /3
B. 84.5
C. 75*sqrt3
D. 169*sqrt3 /4
E. 225*sqrt3 /4

Can anyone explain how to solve this? Thanks

[size=Normal][/size]

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
neelgandham Community Manager
Joined
13 May 2011
Posted:
1060 messages
Followed by:
46 members
Thanked:
305 times
Test Date:
October 15th 2012
Target GMAT Score:
740
Thu Jan 05, 2012 4:16 am
If
A = Length of the side of the equilateral triangle
H = Height of the equilateral triangle

H = length of line segment PQ = Square root((-2+7)^2 + (9+3)^2) = 13
Area of equilateral triangle = H^2/√3 = 169/√3 = 169*√3/3 Option A

note 1: If (x1,y1) and (x2,y2) are two points in the coordinate system, then the distance between two points would be d = sqrt((x1 - x2)^2 + (y1 - y2)^2).
note 2: H = (√3/2)*A => A = (2/√3)*H. Area of triangle = (1/2)*A*H = (1/2)*(2/√3)*H*H = H^2/√3

_________________
Anil Gandham
Welcome to BEATtheGMAT
My Quant Blog | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/

Thanked by: lola27
lola27 Just gettin' started!
Joined
22 Mar 2010
Posted:
3 messages
Thu Jan 05, 2012 4:44 am
Thanks neelgandham. i guess i need to learn those too rules. i didn't know the distance between two points formula

neelgandham Community Manager
Joined
13 May 2011
Posted:
1060 messages
Followed by:
46 members
Thanked:
305 times
Test Date:
October 15th 2012
Target GMAT Score:
740
Thu Jan 05, 2012 5:41 am
Here are some formulae, you might want to learn.

1) A Circle in the coordinate system with center (a,b) and radius r can be represented by the equation
(x-a)^2 + (y-b)^2 = (r^2)

2) Coordinates of the midpoint (X,Y) of the line segment PQ, where point P = (x1,y1) and point Q =(x2,y2), are X =(x1+x2)/2 and Y =(y1+y2)/2.

3) Slope m, is a measure of the steepness of the line, is denoted by (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are points on the line.

4) y = mx+c is the point intercept form of the line equation, Where m is the slope of the line; c is the y-intercept of the line

5) Equation of a vertical line, x=a (where a is a constant)

6) Equation of a vertical line, y=a (where a is a constant)

_________________
Anil Gandham
Welcome to BEATtheGMAT
My Quant Blog | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/

Thanked by: ariz

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
6083 messages
Followed by:
1033 members
Thanked:
5244 times
GMAT Score:
790
Thu Jan 05, 2012 7:03 am
lola27 wrote:
The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateral triangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?

A. 169*sqrt3 /3
B. 84.5
C. 75*sqrt3
D. 169*sqrt3 /4
E. 225*sqrt3 /4

Can anyone explain how to solve this? Thanks

[size=Normal][/size]
To determine the distance between 2 points, make the distance the hypotenuse of a right triangle.
Then apply the pythagorean formula or -- better yet -- look for a special triangle:

Since PQ is the hypotenuse of a 5-12-13 triangle, PQ=13.

The height of an equilateral triangle creates a 30-60-90 triangle:

The sides of a 30-60-90 triangle are proportioned s : s√3 : 2s.
In ∆WXY, s√3 = 13.
Thus, s = 13/√3 and 2s = 26/√3.
Area = (1/2)bh = (1/2)(26/√3)(13) = 169/√3 = (169√3) / (√3*√3) = (169√3)/3.

Note that the solution above does not require knowledge of any special formulas.
While knowing formulas can be be helpful, very few are needed to solve most GMAT problems.
Two important take-aways:

2. LOOK for special triangles.

These two strategies -- all by themselves -- are sufficient to solve many GMAT problems.

_________________
Mitch Hunt
GMAT Private Tutor and Instructor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Contact me about long distance tutoring!

Thanked by: lola27
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

### Best Conversation Starters

1 varun289 43 topics
2 greenwich 30 topics
3 sana.noor 21 topics
4 guerrero 20 topics
5 killerdrummer 19 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

202 posts
2 GMATGuruNY

The Princeton Review Teacher

143 posts
3 Anju@Gurome

Gurome

134 posts
4 Jim@StratusPrep

Stratus Prep

86 posts
5 David@VeritasPrep

Veritas Prep

41 posts
See More Top Beat The GMAT Experts