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December 8th, 2012, 11:45 AM  #1 
Senior Member Joined: Jan 2012 Posts: 720 Thanks: 7  Area of the frame
A rectangular picture 6cm by 8cm is enclosed by a frame 1/2cm wide, calculate the area of the frame. How do I go about it? The area of the picture is (6*cm^2 = 48cm^2. The width of the frame is 1/2. How do I get the length so that I can get the area of the frame? 
December 8th, 2012, 12:52 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,448 Thanks: 565  Re: Area of the frame Quote:
The four corner pieces are each (1/2)(1/2), so total area of corners = 1 cm^2. Entire frame has area 15 cm^2. Alternative method  Frame + picture is 7x9 cm^2, subtract picture area to get 15 cm^2.  
December 8th, 2012, 12:54 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,697 Thanks: 1524 
The combined picture and frame is presumably rectangular, measuring 7cm by 9cm, and so having area 63cm². Hence the frame by itself has area 15cm². (Ah, [color=#00AA00]mathman[/color] got there first). 
December 8th, 2012, 02:07 PM  #4 
Senior Member Joined: Jan 2012 Posts: 720 Thanks: 7  Re: Area of the frame
@mathman I am getting confused the more. How can the total area be 7*9? How did you compute total length of to be 9cm? How did you compute the total width to be 7cm? Men I must confess, I am getting confused the more. 
December 8th, 2012, 03:01 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,697 Thanks: 1524 
The frame adds 1/2 cm on either side and above and below. Hence 2 times 1/2 cm needs to be added to the dimensions of the picture.

December 8th, 2012, 09:08 PM  #6 
Senior Member Joined: Jan 2012 Posts: 720 Thanks: 7  Re: Area of the frame
@Skipjack But the question says that the frame has a width of 1/2cm. Well I am not trying to doubt what you have said. I'm only trying to understand the concept very well. How do I know that know that 1/2cm is added to the either length and breadth of the picture? 
December 9th, 2012, 04:04 AM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,829 Thanks: 761  Re: Area of the frame
Chikis, got ruler, pencil, paper? Draw a 7 by 9 rectangle. Inside it, draw a 6 by 8 rectangle; both rectangles have same center. Good nuff? 
December 9th, 2012, 09:39 AM  #8 
Senior Member Joined: Jan 2012 Posts: 720 Thanks: 7  Re: Area of the frame
@dennis What if the question is changed a bit such that only the length of the frame is given as 1/2cm. How do we get the area of the frame? Will the area of the frame still remain as 15cm^2? 
December 9th, 2012, 09:44 AM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,829 Thanks: 761  Re: Area of the frame
...hope you're not joking... Chikis, get ruler, pencil, paper again! Draw a 8 by 10 rectangle. Inside it, draw a 7 by 9 rectangle; both rectangles have same center. Good nuff? 
December 9th, 2012, 09:47 AM  #10  
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Area of the frame Quote:
 

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