Triangle ABD is a right triangle with two legs 6 and 8, making the hypotenuse 10 (6:8:10 trio).
Since ED=5, it follows that AE is also 5, and each of the is half of the hypotenuse AD.
Several ways you can go from here:
1) small triangle EDC and large triangle ABD are similar (all angles are equal), which means that all their respective sides maintain the same linear ratio. If the hypotenuses have a 5:10 ratio, then the bases EC and AB also maintain the same 1:2 ratio. If AB=6, it follows that EC=3, and if BD=8, then BC=4.
You now have the bases and height of the trapezoid, so you can use the area formula (avg of bases*height) = (6+3)/2 * 4 = 4.5*4 = 18.
2) triangles AFE and CDE are equal. Area of the required quad = area of rectangle - area of triangle AFE, which you have as 4*3/2 = 6. So area of quad is 24-6 = 18.
For Geometry Lovers 2
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Dani@MasterGMAT
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