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The area of each of the 16 square regions in the figure abov

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The area of each of the 16 square regions in the figure abov [#permalink] New post 09 Sep 2013, 23:30
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The area of each of the 16 square regions in the figure above is T. What is the area of the shaded region?

A. \frac{13T}{3}

B. 5T

C. \frac{16T}{3}

D. \frac{11T}{2}

E. 7T

[Reveal] Spoiler:
Please provide detailed explanations!
[Reveal] Spoiler: OA

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Last edited by Bunuel on 09 Sep 2013, 23:55, edited 1 time in total.
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Re: The area of each of the 16 square regions in the figure abov [#permalink] New post 10 Sep 2013, 00:03
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fozzzy wrote:
Image
The area of each of the 16 square regions in the figure above is T. What is the area of the shaded region?

A. \frac{13T}{3}

B. 5T

C. \frac{16T}{3}

D. \frac{11T}{2}

E. 7T

[Reveal] Spoiler:
Please provide detailed explanations!



The whole area = 16T.

The areas of three unshaded triangles are = T + 6T + 4T = 11T (half of a rectangle with area of 2 + half of a rectangle with area of 12 + half of a rectangle with area of 8).

The area of the shaded region = 16T - 11T = 5T.

Answer: B.

Similar question to practice: what-is-the-area-of-a-triangle-with-the-following-vertices-125983.html
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Re: The area of each of the 16 square regions in the figure abov [#permalink] New post 10 Sep 2013, 00:21
So basically what you have done is count the squares and calculated the area's I have modified the image and added color ( Red,Black and blue) so

Black has 4*2*1/2
Red has 4*3*1/2
Blue has 2*1*1/2

is this correct and then subtract from the total?
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Last edited by fozzzy on 10 Sep 2013, 04:27, edited 1 time in total.
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Re: The area of each of the 16 square regions in the figure abov [#permalink] New post 10 Sep 2013, 00:23
Expert's post
fozzzy wrote:
So basically what you have done is count the squares and took the area's I have modified the image and added color ( Red,Black and blue) so

Black has 4*2*1/2
Red has 4*3*1/2
Blue has 2*1*1/2

is this correct and then subtract from the total?


Yes, that's correct.
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Re: The area of each of the 16 square regions in the figure abov [#permalink] New post 19 Nov 2013, 22:05
16T-[(\frac{1}{2}*2\sqrt{T}*\sqrt{T})+(\frac{1}{2}*4\sqrt{T}*3\sqrt{T})+(\frac{1}{2}*2\sqrt{T}*4\sqrt{T})] = 5T
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Re: The area of each of the 16 square regions in the figure abov [#permalink] New post 07 Mar 2014, 06:43
Bunuel.. can you please elaborate on "The areas of three unshaded triangles are = T + 6T + 4T = 11T (half of a rectangle with area of 2 + half of a rectangle with area of 12 + half of a rectangle with area of 8)."
I not able to follow this part.
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Re: The area of each of the 16 square regions in the figure abov [#permalink] New post 07 Mar 2014, 16:58
Option B.
Let T be any convenient no. say 36.
Side of each smaller square=6
Side of bigger square=6*4=24
Area shaded=24^2-(area of 3 unshaded right triangles)
=576-36-144-216
=180
Which is 5*36
Ans:5T

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Re: The area of each of the 16 square regions in the figure abov [#permalink] New post 08 Mar 2014, 04:57
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satsymbol wrote:
Bunuel.. can you please elaborate on "The areas of three unshaded triangles are = T + 6T + 4T = 11T (half of a rectangle with area of 2 + half of a rectangle with area of 12 + half of a rectangle with area of 8)."
I not able to follow this part.

Attachment:
Untitled.png
Untitled.png [ 32 KiB | Viewed 428 times ]


The areas of three unshaded triangles are =
Half of the area of blue rectangle with area of 2T , thus T;
Half of the area of black rectangle with area of 8T , thus 4T.
Half of the area of red rectangle with area of 12T , thus 6T.

T + 4T + 6T = 11T.

Hope it's clear.
_________________

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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 area of each of the 16 square regions in the figure abov   [#permalink] 08 Mar 2014, 04:57
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