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# polygon

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Manager
Joined: 14 Jul 2010
Posts: 72

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15 Aug 2010, 06:57
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I admit its a bad drawing This is an equilateral with an area of 42. C is the midpoint. What is length from A to B
Intern
Joined: 15 Aug 2010
Posts: 23
Location: Mumbai
Schools: Class of 2008, IIM Ahmedabad

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15 Aug 2010, 12:55
Hi,

Let us assume the figure to be ACBDEF.

There are two equal trapeziums ACEF and CBDE.

If a is one of the sides of this figure,

base of trapezium = a units

height of trapezium = (a/2) units

Why? Because
side opposite 30 degrees : side opposite 90 degrees = 1:2 in the 30-60-90 triangle.

Area of the trapezium = base * height = (a^2) / 2 sq units.

Area of the whole figure = (a^2) sq units = 42 sq units.

a = root(42) units.

AB = 2 times height of each trapezium = 2 times (a/2) = a units = root(42) units.

Hope this helps. Is this correct ... Look forward to know a better method.

Thanks.
_________________

Naveenan Ramachandran
4GMAT - Mumbai

Re: polygon   [#permalink] 15 Aug 2010, 12:55
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