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September 4th, 2012, 07:42 PM  #1 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Area of triangle ABC
[attachment=0:y2tsqyu1]Area of triangle ABC.JPG[/attachment:y2tsqyu1]

September 4th, 2012, 09:23 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 462 Math Focus: Calculus/ODEs  Re: Area of triangle ABC
Using coordinate geometry: Orient the coordinate axes such that D is the origin. Then we have A(3,3), B(0,5) and C(5,0), and the area A of the triangle ABC is then: 
September 5th, 2012, 03:19 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 17,910 Thanks: 1382 
AD and BC are parallel, so area of triangle ABC = area of triangle DBC = 25/2.

September 5th, 2012, 04:40 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,457 Thanks: 693  Re: Area of triangle ABC
Total area (including triangle ABH) = 25 + 9 + 3 = 37 "White area" = 5*5/2 + 3*8/2 = 24.5 "Yellow area" = 37  24.5 = 12.5 How come such an easy one, Albert; feeling guilty? 
September 5th, 2012, 05:17 PM  #5 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Area of triangle ABC
Here is a vectored approach. BD+DC=BC. BH+HA=BA. Then the area is 1/2*BA x BC. You can do it from any of the points of the triangle and with different choices of direction.

September 5th, 2012, 06:09 PM  #6  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Area of triangle ABC Hello, Albert.Teng! Quote:
[color=beige]. . . . . . . . . . . [/color]  
September 5th, 2012, 06:18 PM  #7  
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: Area of triangle ABC Quote:
guilty. Do you like easy ones or questions with challenging?  
September 5th, 2012, 07:29 PM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,457 Thanks: 693  Re: Area of triangle ABC
NO easy ones please!

September 6th, 2012, 12:49 AM  #9 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Area of triangle ABC [color=#000000]Another solution (similar to soroban's).[/color] 
September 6th, 2012, 03:00 AM  #10  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Area of triangle ABC Quote:
By pythagoras, By heron, I like skipjack approach, he slides point A to point D along AD and yellow area never changes.  

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