Geometry & Mensuration
Aptitude

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Q.

The trapezoid shown in the given figure 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?

Image for Geometry and Mensuration, Aptitude:2180-1

 A.

39

 B.

40

 C.

42

 D.

45

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Solution:
Option(C) is correct

The formula for calculating the area of a trapezoid is

\(Area=\dfrac{1}{2}(\text{base1}+\text{base2})(height)\)

Answer image for Geometry and Mensuration, Aptitude:2180-1

The bases of the trapezoid are given as 2 feet and 5 feet, so only the height (\(AQ\)) needs to be found.
Since the dashed line \(AB=13\) feet, and triangle \(BQA\) is a right triangle, use the Pythagorean theorem to calculate \(AQ\).Thus,

\(AQ=\sqrt{{13^2-5^2}}\)

\(=\sqrt{144}\)

\(=12\)

Substituting the values into the formula for calculatingthe area of a trapezoid:

\(Area=\dfrac{1}{2}(2+5)(12)\)

\(= 42 \text{ square feet}\)

 


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