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The trapezoid shown in the figure above represents a cross

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The trapezoid shown in the figure above represents a cross [#permalink] New post 19 Dec 2012, 04:18
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Question Stats:

88% (02:21) correct 12% (01:45) wrong based on 246 sessions
Attachment:
Trapezoid.png
Trapezoid.png [ 6.67 KiB | Viewed 4651 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
[Reveal] Spoiler: OA
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Re: The trapezoid shown in the figure above represents a cross [#permalink] New post 19 Dec 2012, 04:23
Expert's post
Image
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
Trapezoid2.png [ 9.67 KiB | Viewed 4100 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.
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Re: The trapezoid shown in the figure above represents a cross [#permalink] New post 28 Aug 2013, 23:24
why AC is height here??? couldnt get it
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Re: The trapezoid shown in the figure above represents a cross [#permalink] New post 29 Aug 2013, 00:51
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Re: The trapezoid shown in the figure above represents a cross [#permalink] New post 29 Aug 2013, 21:57
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Bunuel wrote:
Image
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.
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Re: The trapezoid shown in the figure above represents a cross [#permalink] New post 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
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Re: The trapezoid shown in the figure above represents a cross [#permalink] New post 10 Sep 2013, 10:25
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


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. :|
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Re: The trapezoid shown in the figure above represents a cross [#permalink] New post 11 Sep 2013, 01:54
Expert's post
aakrity wrote:
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


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. :|


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?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: The trapezoid shown in the figure above represents a cross [#permalink] New post 11 Sep 2013, 03:57
Bunuel wrote:
aakrity wrote:
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


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. :|


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
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Re: The trapezoid shown in the figure above represents a cross [#permalink] New post 10 Jul 2014, 09:05
See Image for half triangle + rectangle solution.
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Re: The trapezoid shown in the figure above represents a cross   [#permalink] 10 Jul 2014, 09:05
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