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 Post subject: Area problem
PostPosted: Wed Dec 02, 2015 5:22 pm 
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Joined: Thu Nov 19, 2015 8:09 pm
Posts: 10
Hello!
Does anybody have any ideas about this area problem? It is supposed to be for 10 year olds. Thank you!

Two identical size squares with sides of length 10 centimeters overlap to form a red shaded region as shown. A corner of one square lies at the intersection of the diagonals of the other square. Find the area of the shaded region, in sq cm. (question 1E if you want to see the picture)

http://www.namschool.org/newwebsite/PDF%20Files/MathOlympiad/Summer2013-M1.pdf


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 Post subject: Re: Area problem
PostPosted: Wed Dec 02, 2015 5:33 pm 
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Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11956
Yes - think about dropping a line from the centre of the right hand square to its edge and another from the same place to the left side. Two little triangles are formed - one inside the shaded bit and one outside ... can you see how that helps?


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 Post subject: Re: Area problem
PostPosted: Wed Dec 02, 2015 6:36 pm 
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Joined: Sun Oct 19, 2014 11:52 am
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25 sq cm... I think the red shaded area will remain same if we move the outer square... so imagine its straightened up a bit... the shape so formed will be a red square of 5cm side.


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 Post subject: Re: Area problem
PostPosted: Wed Dec 02, 2015 7:07 pm 
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Joined: Thu Nov 19, 2015 8:09 pm
Posts: 10
Yes, it is always a quarter of a square but I wonder if you need to write it as an equation. Thank you for the replies!


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