March 19th, 2013, 05:36 AM  #1 
Senior Member Joined: Sep 2012 Posts: 199 Thanks: 1  Area problem
I am having problem with this question, I am not 100% that I have worked it out the right way. Question: An enclosure PQRS is to be made as shown, in the figure ( my diagram ). PQ and RQ are fences of total length of 300m. The other two sides are hedges. The angles at Q and R are right angles and the angle at S is 135 degree. The length of QR is x meters. a) show that the area, A m^2, of the enclosure is given by: I will show my working in steps: 1. So after this I have to find the area so what is did was 2. take my red triangle I have the opposite of length x and a angle of I then used this to workout the hypotenuse. 3.hypotenuse 4. I then workout the adjacent So the area of the red triangle 5. I then workout the area of the rectangle what did then was take the area of the rectangle and minus the area of the triangle 6. This gives the right ans, but I don't think what I have done correct, or if I have is there a quicker way, I did spot that I could have used area of trapezium but was not really sure how to apply that. Could someone please point out anywhere I have gone wrong or even show another way around this question. 
March 19th, 2013, 06:52 AM  #2 
Senior Member Joined: Sep 2012 Posts: 199 Thanks: 1  Re: Area problem
Right I have over complicated things slight, just realised that because it's a 45 degree triangle adjacent and opposite will be the same length.

March 19th, 2013, 09:24 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,663 Thanks: 697  Re: Area problem
Can't see your diagram (except top part) 
March 19th, 2013, 10:20 AM  #4 
Senior Member Joined: Sep 2012 Posts: 199 Thanks: 1  Re: Area problem
Strange I will try repost the diagram. I have notice I have smiles in my first post which I did not put in there. Has my post been edit?

March 19th, 2013, 10:47 AM  #5 
Senior Member Joined: Sep 2012 Posts: 199 Thanks: 1  Re: Area problem
It seem to be okay to me, I just double clicked on the diagram. Have another go other wise, I will take a photo on the diagram out of my book a post it up. Problem is not to sure how good the quality will be.

March 19th, 2013, 10:54 AM  #6 
Senior Member Joined: Sep 2012 Posts: 199 Thanks: 1  Re: Area problem
Here is photo out of book. Not great but best I could do.

March 19th, 2013, 11:14 AM  #7 
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 problem
[attachment=0cyy7l7y]as.png[/attachmentcyy7l7y] . 
March 19th, 2013, 11:59 AM  #8 
Senior Member Joined: Sep 2012 Posts: 199 Thanks: 1  Re: Area problem
That's what I got the first time I did the question. But it say I should show the area to be .

March 19th, 2013, 12:15 PM  #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 problem [color=#000000] Quote:
 
March 19th, 2013, 12:54 PM  #10 
Senior Member Joined: Sep 2012 Posts: 199 Thanks: 1  Re: Area problem
Okay no worries. Could you expand on you method a bit more. I see you have add the areas, where I worked out the whole area of the rectangle and then misused the area for the triangle. Yet will still have the same ans. I think the bit that is confusing is where did you get the (3002x) from? Thank by the way for the help. 

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