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

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