The trapezoid shown in the figure above represents a cross : Problem Solving (PS)

My Profile Logout

Test's Subscription Expires:

My Follow Feed Kudos My Error Log

Messages and Replies

Settings Mark All Read

See All

Applicant Notifications

Settings Mark All Read

See All

Global notifications

Settings Mark All Read

See All

The trapezoid shown in the figure above represents a cross

Sort by Date

Sort by Kudos

Author

Message

TAGS:

Hide Tags

Manager

Joined: 02 Dec 2012

Posts: 174

The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

19 Dec 2012, 04:18

00:00

Difficulty:

5% (low)

Question Stats:

87% (01:47) correct

13% (02:27) wrong

based on 823 sessions

HideShow timer Statistics

Attachment:

Trapezoid.png [ 6.67 KiB | Viewed 25355 times ]

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

Spoiler: OA

Math Expert

Joined: 02 Sep 2009

Posts: 53066

Re: The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

19 Dec 2012, 04:23

Attachment:

Trapezoid2.png [ 9.67 KiB | Viewed 21846 times ]

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern

Joined: 02 May 2013

Posts: 1

Re: The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

28 Aug 2013, 23:24

why AC is height here??? couldnt get it

Math Expert

Joined: 02 Sep 2009

Posts: 53066

Re: The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

29 Aug 2013, 00:51

nahianegmat wrote:

why AC is height here??? couldnt get it

Rotate the figure:

Attachment:

Untitled.png [ 6.29 KiB | Viewed 20820 times ]

Hope it's clear.
_________________

Intern

Joined: 01 Jun 2010

Posts: 38

Re: The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

29 Aug 2013, 21:57

Bunuel wrote:

Attachment:

Trapezoid2.png

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.
_________________

Please don't forget to give kudos if you found someone's post helpful. Everyone likes kudos!

Manager

Joined: 25 Sep 2012

Posts: 243

Location: India

Concentration: Strategy, Marketing

Schools: Northeastern '18 (WL), Weatherhead '18 (A$)

GMAT 1: 660 Q49 V31

GMAT 2: 680 Q48 V34

Re: The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

29 Aug 2013, 23:02

Well I don't know the formula for calculating the area of trapezoid. Also, I like to solve sums without using paper pen and with few basic formulae.

I first found out the base (the bottomline in the question figure) using pythogoras triplet (5-12-13).
Then I imagined the figure as right-angled triangle sitting on top of a rectangle.
A(Triangle) = 1/2*3*12 +
A(Rectangle) = 2*12
Total = 42.
I don't know how to insert figures here so can't explain properly

Intern

Joined: 08 Oct 2011

Posts: 36

Re: The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

10 Sep 2013, 10:25

Walkabout wrote:

Attachment:

Trapezoid.png

If the trapezoid represents a cross section of the rudder of a ship, then the area of the cross section of the rudder in square feet should have been the area of both the triangles represented in the figure. I know I am obviously wrong here but the way I mentioned is stuck in my head.

Math Expert

Joined: 02 Sep 2009

Posts: 53066

Re: The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

11 Sep 2013, 01:54

aakrity wrote:

Walkabout wrote:

Attachment:

Trapezoid.png

That's not wrong at all. But the area of a trapezoid can also be found with the direct formula as shown in posts above. If you expand that formula you'll see that you basically get the sum of the areas of the two triangles.

Does this make sense?
_________________

Intern

Joined: 08 Oct 2011

Posts: 36

Re: The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

11 Sep 2013, 03:57

Bunuel wrote:

aakrity wrote:

Walkabout wrote:

Attachment:

Trapezoid.png

That's not wrong at all. But the area of a trapezoid can also be found with the direct formulas as shown in posts above. If you expand that formula you'll see that you basically get the sum of the areas of the two triangles.

Does this make sense?

Oh right. Thank you. That is some relief definitely ! :-D

Intern

Joined: 10 Apr 2012

Posts: 22

Concentration: Finance, Economics

GMAT 1: 760 Q50 V44

Re: The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

10 Jul 2014, 09:05

See Image for half triangle + rectangle solution.

Attachments

Rudder.jpg [ 31.57 KiB | Viewed 18437 times ]

Target Test Prep Representative

Status: Founder & CEO

Affiliations: Target Test Prep

Joined: 14 Oct 2015

Posts: 4972

Location: United States (CA)

Re: The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

23 Jun 2016, 08:28

Walkabout wrote:

Attachment:

Trapezoid.png

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 is the side that 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 is C.
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

TRY FOR $1

CEO

Joined: 11 Sep 2015

Posts: 3447

Location: Canada

The trapezoid shown in the figure above represents a cross [#permalink]

Show Tags

Updated on: 16 Apr 2018, 11:13

Top Contributor

Walkabout wrote:

Attachment:

Trapezoid.png

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

Answer: C

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com