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16 Aug 2019, 02:41
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D
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Difficulty:
25%
(medium)
Question Stats:
74% (01:21) correct
26%
(01:35)
wrong
based on 106
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In quadrilateral ABCD above, CD is parallel to and is longer than AB. What is the area of ABCD?
(1) EC = 75 meters
(2) \(BC = 30\sqrt{10}\) meters
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16 Aug 2019, 02:54
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IMO the answer should be D.
Area of a trapezoid = (sum of || sides)* height/2
We have the height and length of 1 side. All we need is to figure out the other side.
AD
BCE
Statement 1 : EC = 75 -> Sufficient
We get the complete length of the other parallel side.
Cross off options B, C and E.
AD
BCE
Statement 2 : BC=30√10 meters -> Sufficient
Draw a line perpendicular to line CD from B. Let's call the intersection of the perpendicular line to CD be point F. Now BF = AE, since AB || CD.
So in right angled triangle BCF, we know the 2 sides, so we can calculate the third side(x).
The 2nd || line CD lenght = 40 + EF + x
So it's sufficient to calculate the area of the trapezoid.
Cross off option A.
AD
BCE
Final answer option D.
Area of a trapezoid = (sum of || sides)* height/2
We have the height and length of 1 side. All we need is to figure out the other side.
AD
BCE
Statement 1 : EC = 75 -> Sufficient
We get the complete length of the other parallel side.
Cross off options B, C and E.
AD
Statement 2 : BC=30√10 meters -> Sufficient
Draw a line perpendicular to line CD from B. Let's call the intersection of the perpendicular line to CD be point F. Now BF = AE, since AB || CD.
So in right angled triangle BCF, we know the 2 sides, so we can calculate the third side(x).
The 2nd || line CD lenght = 40 + EF + x
So it's sufficient to calculate the area of the trapezoid.
Cross off option A.
Final answer option D.
18 Sep 2019, 00:05
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Bunuel
Official Explanation
We have a trapezoid here. Its area is the height times the average of the two bases, which are AB and CD. We have the height and the length of AB, but not the complete length of CD. On to the statements, separately first.
Statement (1) gives us EC, so we have the measure of the base CD now. Sufficient.
Statement (2) gives us BC. If you imagine a height from point B down to the base (call that point on the base point F), then BCF will be a right triangle with hypotenuse given in Statement (2) and height equal to 90 meters. We can find the length of CF using the Pythagorean Theorem. EF is equal to AB, so we will then have the component parts of CD. Sufficient.
The correct answer is (D).
