Area of triangular region

This topic has expert replies
Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Fri Aug 28, 2009 10:28 am

Area of triangular region

by ferpape » Thu Sep 03, 2009 4:30 pm
In the figure attached, the radius of the circle with center O is 1 and BC=1. What is the area of triangular region ABC?

a) square root of 2 /2
b) square root of 3 /2
c) 1
d) square root of 2
e) square root of 3

Help!
Attachments
figure.png

Master | Next Rank: 500 Posts
Posts: 175
Joined: Mon Feb 09, 2009 3:57 pm
Thanked: 4 times

by tom4lax » Thu Sep 03, 2009 6:31 pm
IMO ans is B.

Since line is the diameter, triangle is 90deg. given two lines of hyp. 2 and short leg 1, we can assume its 30 60 90 triangle, so third leg is root3. 1/2 * root3 * 1 = answer of B

Newbie | Next Rank: 10 Posts
Posts: 7
Joined: Thu Sep 03, 2009 5:45 am
Thanked: 2 times

by Gladiator » Thu Sep 03, 2009 6:35 pm
Any angle formed in a semi-circle is a right angle triangle.

So angle(BCA)=90

so BC =1 and AB=2..using hyp theorem = CA = sqrt(4-1)=sqrt(3)

So area = 1/2 * 1 * sqrt(3)

B is answer

Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Fri Aug 28, 2009 10:28 am

by ferpape » Fri Sep 04, 2009 8:01 am
Im not sure how you calculated the area of CA??

I'll appriciate your comments.

Master | Next Rank: 500 Posts
Posts: 125
Joined: Sun Sep 16, 2007 1:38 pm
Thanked: 6 times

by chetanojha » Fri Sep 04, 2009 1:03 pm
ferpape wrote:Im not sure how you calculated the area of CA??

I'll appriciate your comments.
Check image.
Attachments
triangle.JPG

User avatar
Legendary Member
Posts: 934
Joined: Tue Nov 09, 2010 5:16 am
Location: AAMCHI MUMBAI LOCAL
Thanked: 63 times
Followed by:14 members

by [email protected] » Wed Jun 08, 2011 1:43 am
Answer is B. Explanation:

AC^2 - BC^2 = AB^2
(2)^2 - (1)^2 = 4 - 1 = 3 = square root of 3

Therefore, area of the triangle = 1/2 X Base X Height
= 1/2 X 1 X square root of 3
IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.