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In the figure above, all triangles have the same area. If the area of

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In the figure above, all triangles have the same area. If the area of  [#permalink]

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New post 11 Nov 2017, 06:57
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In the figure above, all triangles have the same area. If the area of the shaded region is 84, and the area of square PQRS is 100, what is the total area of the regions outlined by the heavy line?

(A) 16
(B) 92
(C) 108
(D) 116
(E) 132

Attachment:
2017-11-11_1745_002.png
2017-11-11_1745_002.png [ 53.1 KiB | Viewed 720 times ]

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Re: In the figure above, all triangles have the same area. If the area of  [#permalink]

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New post 11 Nov 2017, 07:55
1
Bunuel wrote:
Image
In the figure above, all triangles have the same area. If the area of the shaded region is 84, and the area of square PQRS is 100, what is the total area of the regions outlined by the heavy line?

(A) 16
(B) 92
(C) 108
(D) 116
(E) 132

Attachment:
2017-11-11_1745_002.png

The area of the shaded region is the area of the square minus 4 of the 8 triangles with the same area. So

The (area of the shaded region) equals the (area of the square) minus (\(\frac{1}{2}\) the area of all the congruent triangles), \(\frac{1}{2}T\):
\(84 = 100 - \frac{1}{2}T\)
\(\frac{1}{2}T = (100 - 84) = 16\)

The area enclosed by the thick outline equals the square plus \(\frac{1}{2}\) the area of the all the triangles:
Area = \(100 + \frac{1}{2}T\)
\(\frac{1}{2}T = 16\)

Area enclosed by thick outline = \(100 + 16 = 116\)

Answer D
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Re: In the figure above, all triangles have the same area. If the area of  [#permalink]

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New post 11 Nov 2017, 08:02
1
Bunuel wrote:
Image
In the figure above, all triangles have the same area. If the area of the shaded region is 84, and the area of square PQRS is 100, what is the total area of the regions outlined by the heavy line?

(A) 16
(B) 92
(C) 108
(D) 116
(E) 132

Attachment:
2017-11-11_1745_002.png


Area of shaded region + Area of 4 Triangles = Area of the square

So, 84 + Area of 4 Triangles = 100

So, Area of 4 Triangles = 100 - 84

Or, Area of 4 Triangles = 16

Since, Area of each triangle = 4

Since all the triangles are of equal area , the area of the total figure = Area of the square + area of 4 trinagles

Or, Area of the total figure = 100 + 16

Or, Area of the total figure = 116, answer will be (D)

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Re: In the figure above, all triangles have the same area. If the area of  [#permalink]

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New post 19 Nov 2017, 08:05
1
Bunuel wrote:
Image
In the figure above, all triangles have the same area. If the area of the shaded region is 84, and the area of square PQRS is 100, what is the total area of the regions outlined by the heavy line?

(A) 16
(B) 92
(C) 108
(D) 116
(E) 132

Attachment:
2017-11-11_1745_002.png


Bunuel

Can you please explain how come the area is 132?
Is it a wrong OA or something that everyone is missing out on.

Answer clearly seems to be 116.

Please help!
Math Expert
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Joined: 02 Sep 2009
Posts: 47918
Re: In the figure above, all triangles have the same area. If the area of  [#permalink]

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New post 19 Nov 2017, 08:56
GMATAspirer09 wrote:
Bunuel wrote:
Image
In the figure above, all triangles have the same area. If the area of the shaded region is 84, and the area of square PQRS is 100, what is the total area of the regions outlined by the heavy line?

(A) 16
(B) 92
(C) 108
(D) 116
(E) 132

Attachment:
2017-11-11_1745_002.png


Bunuel

Can you please explain how come the area is 132?
Is it a wrong OA or something that everyone is missing out on.

Answer clearly seems to be 116.

Please help!


The OA is D. Edited. Thank you.
_________________

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

Re: In the figure above, all triangles have the same area. If the area of &nbs [#permalink] 19 Nov 2017, 08:56
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