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Area of a Quadrilateral

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Source: — Problem Solving |
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by parallel_chase » Fri Aug 15, 2008 8:04 am
Area ABD = area AECB + area ECD

area ABEC = 1/2 *AB*BD = 1/2 *8*6=24

ED=5
Therefore, CD = 4, EC=3

Area ECD = 1/2*CD*EC = 1/2*4*3 = 6


area AECB = 24-6 =18

Whats the OA?
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by pepeprepa » Fri Aug 15, 2008 8:20 am
I agree with 18.
You can see that AFE and ECD are similar given we know they have two angles in common. Added to the fact they have the same hypothenuse, they are identical.
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by sudhir3127 » Fri Aug 15, 2008 8:31 am
Even i agree with chase...

i go with 18 as well.. same explanation as chase...
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by malolakrupa » Fri Aug 15, 2008 9:32 am
OA is 18. But I did not get the part CD = 4, EC=3 . How did you derive that?

Thanks chase
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by kris610 » Fri Aug 15, 2008 10:41 am
ABD and ECD are similar triangles, which means that the ratio of the corresponding sides will be the same. From the given info, you can calculate AD, from which you can calculate EC and CD. Now compute area of the bigger triangle, and subtract the area of the smaller triangle from that.
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