Problem Solving

GmatGreen wrote:
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)/2
So, 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 = 12

Aside: 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 = C

Cheers,
Brent



So, we

Hi GmatGreen,

Each of the explanations in this string properly shows how to do the "math" behind this question, so I won't rehash that here. Instead I'll offer this takeaway about GMAT Geometry questions: they're almost always based on standard shapes and formulas. Any time you encounter a GMAT question with a non-standard shape, you should think about how you can "break" that shape into pieces that ARE standard shapes. In this question, the trapezoid can be easily broken down into a rectangle and a right triangle. Dealing with those two pieces individually makes this question fairly easy to handle.

GMAT assassins aren't born, they're made,
Rich

GmatGreen wrote:
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

Solution:

Although this problem may seem confusing based on the description of the shape, we must keep in mind that the diagram provided is simply a trapezoid. So when we are asked to determine the area of the "cross section of the rudder," this really means "What is the area of the trapezoid?"

The formula for the area of a trapezoid is:

area = (base 1 + base 2) x height/2

The two bases are given as 2 feet and 5 feet. Because the height is always perpendicular to the base, the height of this particular trapezoid begins at A and ends at the right angle located at the bottom right of the figure. We don't know this value, so we must calculate it. We could use the Pythagorean Theorem to determine the height, but instead we note that we have a 5-12-13 right triangle, where the unknown side (or the height) is 12.

We can now substitute the values for the two bases (2 and 5) and the height (12) into our area equation.

area = (base 1 + base 2) x height/2

area = (2 + 5) x 12/2

area = 7 x 6

area = 42

Answer: C