# Moderate Geometry & Mensuration Solved QuestionAptitude Discussion

 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?
 ✖ A. 39 ✖ B. 40 ✔ C. 42 ✖ D. 45

Solution:
Option(C) is correct

The formula for calculating the area of a trapezoid is

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

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:

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

$= 42 \text{ square feet}$