[42] The trapezoid shown in the given figure represents a cross section of the rudder of a ship.If the di

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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?

Explanation:

The formula for calculating the area of a trapezoid is

$Area=\dfrac{1}{2}\left(base1+base2\right)\left(height\right)$

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:

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

=42 square feet

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