My Math Forum Area of the frame

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 December 8th, 2012, 11:45 AM #1 Senior Member     Joined: Jan 2012 Posts: 721 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
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Re: Area of the frame

Quote:
 Originally Posted by Chikis 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?
The part of the frame directly in contact with the picture has dimensions 2x(6+x(1/2) = 14 cm^2.
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: 18,962 Thanks: 1606 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: 721 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: 18,962 Thanks: 1606 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: 721 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: 12,423 Thanks: 832 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: 721 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: 12,423 Thanks: 832 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
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Re: Area of the frame

Quote:
 Originally Posted by Chikis @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?
Knowing that the frame is 1/2cm wide allows you to compute the area of picture plus frame, hence get the area of just the frame by subtracting the area of the picture, as several have explained. In your new case, we are missing information.

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# A rectangular picture 6cn by 8cn is enclosed by a franne 1/2cn wide calculate the area of the frane

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