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PostPosted: Sat Dec 10, 2011 7:42 am 
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Joined: Sun Jul 18, 2010 8:02 pm
Posts: 86
square is 3 units long with 4 identical semi-circles drawn on each edge. semi-circles overlap to create 4 petals which are shaded

the area of each semi-circle is 3.5 square units. work out shaded area

sorry can't draw


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PostPosted: Sat Dec 10, 2011 7:59 am 
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Joined: Wed Oct 19, 2011 9:18 pm
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Area of Square = 3 X 3 = 9 square units
Total Area of all semi Circles = 3.5 X 4 = 14 square units

So, Area of shaded portions = 14 - 9 = 5 square units


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PostPosted: Sat Dec 10, 2011 9:31 am 
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thanks for reply

i know i did not draw it but i don't think this is correct

am i wrong twice :oops: :mrgreen:


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PostPosted: Sat Dec 10, 2011 7:43 pm 
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Joined: Sat Jul 31, 2010 3:31 pm
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Hi Minesh!

I just looked at the diagram (on Habs web site) until I noticed that I could calculate the unshaded area in this way:

Look at two opposing semi circles and imagine them completely shaded. Their area total 3.5 x 2 =7. What's left? It's the two bits opposite each other, which must total 9 - 7 = 2 in area.

There are two of these unshaded pairs of shapes, so the total unshaded area is 2 x 2 = 4.

So the shaded area of the petals must be 9 - 4 = 5 sq units.

Different approach, but I agree with the previously posted answer.

By the way, I wonder if even the Scholarship winners will get this! I think I was just lucky to see the solution visually quite quickly today!

WH


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PostPosted: Sat Dec 10, 2011 9:14 pm 
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Your name is befitting - you work hard

thank you very much for taking the trouble to look at diagram and for clear explanation
:D :)


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