Since BE is ll to CD that makes triangle ABE and triangle ACD similar triangles.
Hence AB/AC = AE / AD = BE / CD
now we can get AB=3, AE = 4, BE=5
AC= 6, CD = 10, AD = 8.
Area of triangle ABE = sqrt(s*(s-a)*(s-b)*(s-c)) Where s=(a+b+c)/2.
Solving this we will get
Area of ABE= sqrt 36 = 6
Area of ACD = sqrt 672 = 24
Hence area of Trapezoid BEDC= 18
Ans: B
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Area of the trapeziod
Source: Beat The GMAT — Problem Solving |
Hi,
Mid Point Theorem can be used to solve the above problem:
The straight line joining the mid-points of two sides of a triangle is parallel to and equal to half the third side.
Converse of Mid-Point Theorem
The straight line drawn through the mid-point of one side of a triangle parallel to another, bisects the third side
Hope it is clear...
Mid Point Theorem can be used to solve the above problem:
The straight line joining the mid-points of two sides of a triangle is parallel to and equal to half the third side.
Converse of Mid-Point Theorem
The straight line drawn through the mid-point of one side of a triangle parallel to another, bisects the third side
Hope it is clear...
Anyone from Hyderabad or Telugu speaking community.
Searching for a serious study partner from Hyderabad or the one who work for same Company.
Searching for a serious study partner from Hyderabad or the one who work for same Company.
I have solved it another way...if there is any problem with my approach then please let me know.
AB = BC = 3
Thus AC = 6.
On the other hand, since BE II CD and B is the mid point of AC, E should be the mid point of AD.
Since AE = ED = 4, AD = 8.
Thus the triangle ACD has arms of 6:8:10 and must be a right triangle. LCAD = 90 deg.
Its area should be: 1/2*AC*AD = 24.
On the other hand, area of triangle ABE is : 1/2*AB*AE = 6.
So the difference (answer) = 18 (B)
AB = BC = 3
Thus AC = 6.
On the other hand, since BE II CD and B is the mid point of AC, E should be the mid point of AD.
Since AE = ED = 4, AD = 8.
Thus the triangle ACD has arms of 6:8:10 and must be a right triangle. LCAD = 90 deg.
Its area should be: 1/2*AC*AD = 24.
On the other hand, area of triangle ABE is : 1/2*AB*AE = 6.
So the difference (answer) = 18 (B)
Hi Want to beat...
I think there is no flaw in the way you solved the problem and I would like to appreciate the solution... it is really simple and good.
I think there is no flaw in the way you solved the problem and I would like to appreciate the solution... it is really simple and good.
Anyone from Hyderabad or Telugu speaking community.
Searching for a serious study partner from Hyderabad or the one who work for same Company.
Searching for a serious study partner from Hyderabad or the one who work for same Company.
