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

Attachment:

Trapezoid2.png

The formula for calculating the area of a trapezoid is \(Area=\frac{1}{2}(base_1+base_2)(height)=\frac{1}{2}(2+5)(height)\).

So, we need to find the height AC: \(AC=\sqrt{AB^2-BC^2}=\sqrt{13^2-5^2}=12\).

Therefore, \(Area=\frac{1}{2}(2+5)*12=42\).

Answer: C.

You could save yourself some calculation here if you knew the pythagorean triple 5-12-13. That would shave a few seconds off of the problem.