Walkabout wrote:
Attachment:
Trapezoid.png
The trapezoid shown in the figure above represents a cross section of the rudder of a ship. If the distance from A to B is 13 feet, what is the area of the cross section of the rudder in square feet?
(A) 39
(B) 40
(C) 42
(D) 45
(E) 46.5
Let's add a few things to the diagram to make the solution easier to follow.
Okay, first we should recognize that the two 90-degree angles (at vertices A and D) mean that
sides AC and BD are PARALLEL, which means the rudder (quadrilateral ACBD) is a TRAPEZOID. Area of trapezoid = (sum of the parallel sides)(distance between parallel sides)/2So, all we need to do now is determine the length of side AD.
Now recognize that ∆ABD is a RIGHT TRIANGLE.
So, we can use the Pythagorean Theorem to get the equation: 5² + (AD)² = 13²
Evaluate: 25 + (AD)² = 169
Simplify: (AD)² = 144
Solve:
AD = 12Aside: We could have saved time be recognizing that this is a 5-12-13 (since we already knew the 5 and 13 lengths)
Okay, now that we know the length of side AD, we can find the area of this trapezoid.
Area = (2 + 5)(12)/2
= 42
Answer: C
Cheers,
Brent
_________________
Brent Hanneson – Creator of gmatprepnow.com
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