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The sides of a quadrilateral taken in order are 16,16,14 and
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Updated on: 07 Mar 2004, 13:23
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The sides of a quadrilateral taken in order are 16,16,14 and 10. The angle contained by the frist two sides is 60 degrees. What is teh area of the quadrilateral?
12(sqrt252)
104(sqrt3)
16(sqrt3)(4+sqrt15)
14(sqrt3)+5
what the... == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Originally posted by sunniboy007 on 07 Mar 2004, 12:25.
Last edited by sunniboy007 on 07 Mar 2004, 13:23, edited 1 time in total.



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I dont know how to solve this without knowing the other angles.



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yes, it's a tough bugger!
I will give others a chance to answer it before I post the the official answer and reasoning.
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Pls include reasoning along with all answer posts.
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B it is.......... !!
here's the soln:
1st 2 sides are 16 each and they form angle = 60 degrees
So If u draw a diagonal the triangle that contains diagonal and these 2 sides will be equilateral, with sides 16.
Therefore area of Triangle = (sqrt3/4)*16*16 =64*sqrt3
For the other triangles sides are=16,14,10
Hence its area = 40sqrt3
Area of quad = sum of 2 triangles = 104 sqrt3!!



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cbrf3
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Pls include reasoning along with all answer posts.
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cbrf3 wrote: For the other triangles sides are=16,14,10 Hence its area = 40sqrt3
What is the formula to find the area from the length of sides?



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kpadma wrote: cbrf3 wrote: For the other triangles sides are=16,14,10 Hence its area = 40sqrt3
What is the formula to find the area from the length of sides?
This requires 2 simple pythagorean formulas with 2 unknown. The workout is a bit longer than the simple answer posted by cbrf3 though
We can let base (b) = 16
The height of the second triangle will separate that triangle into 2 right triangles. Let X be the length of the shorter side of the base and (16X) be the length of the longer side of the base.
h^2 = 10^2  X^2
h^2 = 14^2  (16X)^2
100  X^2 = 196  (25632X+X^2)
100  X^2 = 60 + 32X  X^2
32X = 160 > X = 5
Height would be equal to:
h^2 = 10^2  5^2
= 100  25 = 75
h = 5sqrt3
Area of second triangle is b*h/2 = 16*5sqrt3 / 2 = 40sqrt3
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Quote: For the other triangles sides are=16,14,10 Hence its area = 40sqrt3
What is the formula to find the area from the length of sides?
Paul and KPADMA, the formula to find area of a triangle from measures of its sides is:
A = SQRT of (s*(sa)*(sb)*(sc)) ; where s=1/2 (perimeter of triangle)
Hope, this will help
Dharmin



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Dharmin wrote: Quote: For the other triangles sides are=16,14,10 Hence its area = 40sqrt3
What is the formula to find the area from the length of sides? Paul and KPADMA, the formula to find area of a triangle from measures of its sides is: A = SQRT of (s*(sa)*(sb)*(sc)) ; where s=1/2 (perimeter of triangle) Hope, this will help Dharmin
Awesome Dharmin. It sure simplifies things. == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Paul



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Re: The sides of a quadrilateral taken in order are 16,16,14 and
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20 Jan 2019, 21:32
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Re: The sides of a quadrilateral taken in order are 16,16,14 and
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20 Jan 2019, 21:32






